the multifrontal method for sparse matrix solution theory and practice this paper presents an overview of the multifrontal method for the solution of large sparse symmetric positive definite linear systems the method is formulated in terms of frontal matrices update matrices and an assembly tree formal definitions of these notions are given based on the sparse matrix structure various advances to the basic method are surveyed they include the role of matrix reorderings the use of supernodes and other implementatjon techniques the use of the method in different computational environments is also described

brief paper global stabilization of semilinear systems using switching controls this paper considers feedback stabilization of distributed semilinear systems using switching controls the semilinear processes together with the switched controllers constitute a type of switched nonlinear system three kinds of stabilizabilities namely weak strong and exponential stabilizabilities are investigated one by one sets of sufficient conditions are obtained for each case a necessary condition for strong stabilizability is given the stabilizing control is characterized using a minimization problem applications to parabolic and hyperbolic like equations are considered

efficient inversion of the galerkin matrix of general second order elliptic operators with nonsmooth coefficients this article deals with the efficient approximate inversion of finite element stiffness matrices of general second order elliptic operators with l coefficients it will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices h matrices furthermore numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear complexity

sliding mode control in indefinite dimensional systems abstract a mathematical description of motion in a sliding mode is considered for systems with discontinuous controls described by differential equations in banach space applying the regularization principle to such systems the sliding mode equations are obtained for a set of interconnected heat processes the control system with the prescribed dynamics is designed through deliberate introduction of sliding modes

a fast algorithm for sparse multichannel blind deconvolution abstractwe have addressed blind deconvolution in a multichannel framework recently a robust solution to this problem based on a bayesian approach called sparse multichannel blind deconvolution smbd was proposed in the literature with interesting results however its computational complexity can be high we have proposed a fast algorithm based on the minimum entropy deconvolution which is considerably less expensive we designed the deconvolution filter to minimize a normalized version of the hybrid l1 l2 norm loss function this is in contrast to the smbd in which the hybrid l1 l2 norm function is used as a regularization term to directly determine the deconvolved signal results with synthetic data determined that the performance of the obtained deconvolution filter was similar to the one obtained in a supervised framework similar results were also obtained in a real marine data set for both techniques

fundamental initial frequency and frequency rate estimation of random amplitude harmonic chirps we consider the problem of estimating the fundamental initial frequency and frequency rate of a linear chirp with random amplitudes harmonic components we develop an iterative nonlinear least squares estimator which involves a large number of computations as it requires high resolution search in the initial frequency and frequency rate parameter space as an alternative we suggest two suboptimal low complexity estimators the first is based on the high order ambiguity function which reduces the problem to a one dimensional search the second method applies our recently published harmonic separate estimate method which was used for constant amplitude harmonic chirps we present modifications of both methods for harmonic chirps with random amplitudes we also provide a framework for estimating the number of harmonic components numerical simulations show that the iterative nonlinear least squares estimator achieves its asymptotic accuracy in medium to high signal to noise ratio while the two sub optimal low complexity estimators perform well in high signal to noise ratio real data examples demonstrate the performance of the harmonic separate estimate method on random amplitude real life signals

cyclic group and knapsack facets any integer program may be relaxed to a group problem we define the master cyclic group problem and several master knapsack problems show the relationship between the problems and give several classes of facet defining inequalities for each problem as well as a set of mappings that take facets from one type of master polyhedra to another

boundary optimal lq control of coupled hyperbolic pdes and odes this contribution addresses the development of a linear quadratic lq regulator for a set of hyperbolic pdes coupled with a set of odes through the boundary the approach is based on an infinite dimensional hilbert state space description of the system and the well known operator riccati equation ore in order to solve the optimal control problem the ore is converted to a set of matrix riccati equations the feedback operator is found by solving the resulting matrix riccati equations the performance of the designed control policy is assessed by applying it to a system of interconnected continuous stirred tank reactor cstr and a plug flow reactor pfr through a numerical simulation

an cal h 2 matrix based integral equation solver of reduced complexity and controlled accuracy for solving electrodynamic problems using an h 2 matrix as the mathematical framework we compactly represent a dense system matrix by a reduced set of parameters thus enabling a significant reduction in computational complexity the error bound of the h 2 matrix based representation of an electrodynamic problem was derived we show that exponential convergence with respect to the number of interpolation points can be achieved irrespective of the electric size in addition we show that a direct application of h 2 matrix based techniques to electrodynamic problems would result in a complexity greater than o n with n being the matrix size due to the need of increasing the rank when ascending an inverted tree in order to keep a constant order of accuracy a rank function was hence developed to maintain the same order of accuracy in a wide range of electric sizes without compromising computational complexity with this rank function we demonstrate that given a range of electric sizes which lead to a range of n the dense system of o n 2 parameters can be compactly stored in o n units and the dense matrix vector multiplication can be performed in o n operations moreover the same order of accuracy can be kept across this range the method is kernel independent and hence is suitable for any integral equation based formulation in addition it is applicable to arbitrary structures numerical experiments from small electric sizes to 64 wavelengths have demonstrated the performance of the proposed method

exponential stability for a class of boundary conditions on a euler bernoulli beam subject to disturbances via boundary control abstract this paper outlines the procedure for applying a sliding mode backstepping boundary control technique to a euler bernoulli beam subject to unknown bounded disturbances on the boundary for four different types of boundary conditions referred to in this paper as a class of boundary conditions these boundary conditions include all combinations of pinned and sliding types with control and disturbances on one boundary i e pinned pinned pinned sliding sliding pinned and sliding sliding with input on the second boundary the technique was developed for the specific case of a pinned pinned beam in the literature and in this paper the technique is generalized to the degree that it is possible to cover all four of the aforementioned cases furthermore a proof of the fully arbitrary exponential stability of the closed loop system is provided in this paper to this point only asymptotic stability was shown for the closed loop system for one case the technique outlined in this paper provides for a class of boundary conditions a controller that exponentially stabilizes the vibrations in a beam in the presence of bounded unknown disturbances the beam displacement returns to the origin and its decay is bounded by a known exponential decay function after a known finite time reaching phase

a non overlapping domain decomposition method with non matching grids for modeling large finite antenna arrays a non overlapping domain decomposition method ddm is proposed herein to solve maxwell equations in r 3 in this work the maxwell equations are discretized using a vector finite element method with hierarchical h curl vector basis functions there are two major ingredients in the proposed non overlapping ddm a a proper 1st order transmission condition to enforce field continuity across domain boundaries and b a cement technique to allow non matching grids for neighboring domains moreover a detail fourier analysis of the transmission condition for a canonical half space example is presented the analysis provides significant insights into the convergence behavior of the proposed non overlapping ddm for solving electromagnetic radiation problems such as the large finite antenna arrays particularly for the antenna arrays the proposed non overlapping ddm is extremely efficient since the formulation can easily incorporate geometrical repetitions exponentially tapered notch vivaldi antenna arrays with size up to 100x100 elements are solved on a common pc to validate the proposed non overlapping ddm

super resolution of multi observed rgb d images based on nonlocal regression and total variation there is growing demand for accuracy in image processing and visualization and the super resolution sr technique for multi observed rgb d images has become popular because it provides space redundant information and produces a detailed reconstruction even with a large magnification factor this technique has been thoroughly investigated in recent years nevertheless technical challenges remain such as finding sub pixel correspondences with low resolution lr observations exploiting space redundant information formulating space homogeneity constraints and leveraging cross image similarities in structures to address these challenges this paper proposes a unified optimization framework to estimate both the super resolved rgb image and the super resolved depth image from the multi observed lr rgb d images using their correlations using depth assisted cross image correspondences the rgb image sr problem is formulated as an effective regularization function by incorporating the normalized bilateral total variation regularizer and it is efficiently solved by a first order primal dual algorithm the depth image sr estimate can be obtained by minimizing a nonlocal regression based energy which integrates the structural cues of the super resolved rgb image in a detail preserving fashion essentially our unified optimization framework uses the rgb image and depth image as a priori knowledge that the sr process uses for better accuracy our extensive experiments on public rgb d benchmarks and real data and our quantitative comparison with several state of the art methods demonstrate the superiority of our method in terms of accuracy versatility and reliability of details and sharp feature preservation

cyclic group blocking polyhedra gomory linear algebra appl 2 451 558 1969 gave a subadditive characterization of the facets of the group polyhedron although there are exponentially many facets see gomory and johnson in math program 3 359 389 1972 example 4 6 and exponentially many vertices for the group polyhedron for the master cyclic group problem gomory s characterization of the non trivial facets has polynomially many subadditive inequalities in fact of order g 2 for a finite abelian group g we reduce this subadditive inequality system to its minimal representation by a triple system of the same order and show the dimensionality of the polytope of non trivial facets the system of all triples corresponds to all solution vectors of length three into which every solution vector can be decomposed our minimal representation leads to a characterization of the vertices of length three gomory et al math program 96 321 339 2003 introduced a shooting experiment involving solving the shooting linear program repeatedly to find important facets we develop a topological network flow model of the dual problem of the shooting linear program in a reverse procedure from the decomposition of solution vectors into triples hunsaker 2003 gave a knapsack shooting experiment which we use to find a simple pattern for the most hit knapsack facets

on deriving a locally corrected nystrom scheme from a quadrature sampled moment method a novel high order method of moment procedure with quadrature point based discretization is presented the scheme is equivalent to a moment method employing smooth basis and testing functions applying a fixed point numerical quadrature approximation for the outer integral mapping the current to the quadrature points then leads to a formulation that is equivalent to that derived via the locally corrected nystrom method the convergence properties of the current density and rcs for smooth and singular geometries in two and three dimensions are also studied

exponential stability of nondissipative linear system in banach space and application to unbounded bilinear systems abstract we consider linear control systems of the form d z t d t a z t b z t where is a real parameter a is the infinitesimal generator of a linear c 0 semigroup of contractions s 0 t on a banach space x and the linear perturbation b is a relatively bounded operator with respect to a we provide necessary and sufficient conditions for exponential stability of the above system our stability results are then applied to establish uniform exponential stabilization of linear and bilinear systems with unbounded control operators applications to hyperbolic like equations are considered

group level spatial independent component analysis of fourier envelopes of resting state meg data article we developed a data driven method to spatiotemporally and spectrally characterize the dynamics of brain oscillations in resting state magnetoencephalography meg data the method called envelope spatial fourier independent component analysis esfica maximizes the spatial and spectral sparseness of fourier energies of a cortically constrained source current estimate we compared this method using a simulated data set against 5 other variants of independent component analysis and found that esfica performed on par with its temporal variant etfica and better than other ica variants in characterizing dynamics at time scales of the order of minutes

minimal basis subspace representation a unified framework for rigid and non rigid motion segmentation motion segmentation and non rigid structure from motion are two challenging computer vision problems that have attracted numerous research interests while the previous works handle these two problems separately we present a general motion segmentation framework in this paper for solving these two seemingly different problems in a unified manner at the heart of our general motion segmentation framework is a model selection mechanism based on finding the minimal basis subspace representation by seeking the joint sparse representation of the data matrix however such formulation is np hard and we solve the convex proxy instead unlike other compressive sensing related works this convex proxy solution is insufficient for our problem the convex relaxation artefacts and noise yield multiple subspace representations making identification of the exact number of motion subspaces challenging we solve for the right number of subspaces by transforming this problem into a facility location problem with global cost and solve the factor graph formulation using max product belief propagation message passing

hybrid cross approximation of integral operators the efficient treatment of dense matrices arising e g from the finite element discretisation of integral operators requires special compression techniques in this article we use the matrix representation that approximates the dense stiffness matrix in admissible blocks corresponding to subdomains where the underlying kernel function is smooth by low rank matrices the low rank matrices are assembled by a new hybrid algorithm hca that has the same proven convergence as standard interpolation but also the same efficiency as the heuristic adaptive cross approximation aca

dimension reduction with extreme learning machine data may often contain noise or irrelevant information which negatively affect the generalization capability of machine learning algorithms the objective of dimension reduction algorithms such as principal component analysis pca non negative matrix factorization nmf random projection rp and auto encoder ae is to reduce the noise or irrelevant information of the data the features of pca eigenvectors and linear ae are not able to represent data as parts e g nose in a face image on the other hand nmf and non linear ae are maimed by slow learning speed and rp only represents a subspace of original data this paper introduces a dimension reduction framework which to some extend represents data as parts has fast learning speed and learns the between class scatter subspace to this end this paper investigates a linear and non linear dimension reduction framework referred to as extreme learning machine ae elm ae and sparse elm ae selm ae in contrast to tied weight ae the hidden neurons in elm ae and selm ae need not be tuned and their parameters e g input weights in additive neurons are initialized using orthogonal and sparse random weights respectively experimental results on usps handwritten digit recognition data set cifar 10 object recognition and norb object recognition data set show the efficacy of linear and non linear elm ae and selm ae in terms of discriminative capability sparsity training time and normalized mean square error

discontinuous feedback stabilization of minimum phase semilinear infinite dimensional systems with application to chemical tubular reactor this paper develops discontinuous control methods for minimum phase semilinear infinite dimensional systems driven in a hilbert space the control algorithms presented ensure asymptotic stability global or local accordingly as state feedback or output feedback is available as well as robustness of the closed loop system against external disturbances with the a priori known norm bounds the theory is applied to stabilization of chemical processes around prespecified steady state temperature and concentration profiles corresponding to a desired coolant temperature two specific cases a plug flow reactor and an axial dispersion reactor governed by hyperbolic and parabolic partial differential equations of first and second order respectively are under consideration to achieve a regional temperature feedback stabilization around the desired profiles with the region of attraction containing a prescribed set of interest a component concentration observer is constructed and included into the closed loop system so that there is no need for measuring the process component concentration which is normally unavailable in practice performance issues of the discontinuous feedback design are illustrated in a simulation study of the plug flow reactor

a 3 slope theorem for the infinite relaxation in the plane in this paper we consider the infinite relaxation of the corner polyhedron with 2 rows for the 1 row case gomory and johnson proved in their seminal paper a sufficient condition for a minimal function to be extreme the celebrated 2 slope theorem despite increased interest in understanding the multiple row setting no generalization of this theorem was known for this case we present an extension of the 2 slope theorem for the case of 2 rows by showing that minimal 3 slope functions satisfying an additional regularity condition are facets and hence extreme moreover we show that this regularity condition is necessary unveiling a structure which is only present in the multi row setting

mixed integer cuts from cyclic groups we analyze a separation procedure for mixed integer programs related to the work of gomory and johnson on interpolated subadditive functions this approach has its roots in the gomory johnson characterization on the master cyclic group polyhedron to our knowledge the practical benefit that can be obtained by embedding interpolated subadditive cuts in a cutting plane algorithm was not investigated computationally by previous authors in this paper we compute for the first time the lower bound value obtained when adding implicitly all the interpolated subadditive cuts that can be derived from the individual rows of an optimal lp tableau thus approximating the optimization over the intersection of the gomory corner polyhedron with the lp relaxation of the original problem formulation the computed bound is compared with that obtained when only gomory mixed integer cuts are used on a very large test bed of mip instances

blind separation of speech mixtures via time frequency masking binary time frequency masks are powerful tools for the separation of sources from a single mixture perfect demixing via binary time frequency masks is possible provided the time frequency representations of the sources do not overlap a condition we call w disjoint orthogonality we introduce here the concept of approximate w disjoint orthogonality and present experimental results demonstrating the level of approximate w disjoint orthogonality of speech in mixtures of various orders the results demonstrate that there exist ideal binary time frequency masks that can separate several speech signals from one mixture while determining these masks blindly from just one mixture is an open problem we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided motivated by the maximum likelihood mixing parameter estimators we define a power weighted two dimensional 2 d histogram constructed from the ratio of the time frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters the histogram is used to create time frequency masks that partition one of the mixtures into the original sources experimental results on speech mixtures verify the technique example demixing results can be found online at http alum mit edu www rickard bss html

constrained locally corrected nystrom method a generalization of the locally corrected nystrom lcn discretization method is outlined wherein sparse transformations of the lcn system matrix are obtained via singular value decompositions of local constraint matrices the local constraint matrices are used to impose normal continuity of the currents across boundaries shared by mesh elements due to the method s simplicity and flexibility it is straightforward to develop high order constrained lcn clcn systems for different formulations and mesh element types numerical examples demonstrate the memory savings provided by the clcn method and its improved accuracy when applied to geometries with sharp edges it is also shown that the clcn method maintains the high order convergence of the lcn method and it eliminates the need to include line charges in nystrom based discretizations of formulations that involve the continuity equation

discontinuous unit feedback control of uncertain infinite dimensional systems control systems driven by a discontinuous unit feedback in a hilbert space are studied the equation which describes a system motion taking place in the discontinuity manifold and further referred to as a sliding mode is derived by means of a special regularization technique based on the sliding mode equation the procedure of synthesis of a discontinuous unit control signal is developed restricted to a class of infinite dimensional systems with finite dimensional unstable part this procedure generates the control law which ensures desired dynamic properties as well as robustness of the closed loop system with respect to matched disturbances as an illustration of the capabilities of the procedure proposed a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators

reduce and boost recovering arbitrary sets of jointly sparse vectors the rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of nonadaptive linear measurements under appropriate conditions on the measurement matrix the vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern in this paper we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set instead we prove that the entire infinite set of sparse vectors can be recovered by solving a single reduced size finite dimensional problem corresponding to recovery of a finite set of sparse vectors we then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements our approach is exact for both countable and uncountable sets as it does not rely on discretization or heuristic techniques to efficiently find the single sparse vector produced by the last reduction step we suggest an empirical boosting strategy that improves the recovery ability of any given suboptimal method for recovering a sparse vector numerical experiments on random data demonstrate that when applied to infinite sets our strategy outperforms discretization techniques in terms of both run time and empirical recovery rate in the finite model our boosting algorithm has fast run time and much higher recovery rate than known popular methods

sparse matrix factorization using overlapped localizing logos modes on a shifted grid different types of local global solution logos modes have been proposed to develop fast direct solvers for electromagnetic wave problems while radiating logos modes are suitable for high frequency problems this paper focuses on the localizing logos modes which are suitable for low to mid frequency problems factorizations relying on non overlapped localizing logos nl logos modes are provably error controllable but fail to provide acceptable asymptotic computational efficiencies factorizations using overlapped localizing logos ol logos modes provide improved asymptotic computational performance but have been observed to suffer from significant overhead and in some cases poorer error control this paper describes a new procedure for obtaining the ol logos modes it is observed that the asymptotic efficiency is similar to previously reported ol logos schemes while providing stable error control for standard problem formulations the overhead associated with computing the ol logos modes is also reduced significantly

continuous state feedback tracking of an uncertain heat diffusion process a spatially distributed form of a second order sliding mode control algorithm is suggested for the feedback control of a heat process subject to unmeasurable sufficiently smooth persistent disturbances of arbitrary shape in order to obtain a continuous control input while retaining similar properties of robustness as those usually endowing the discontinuous control systems a dynamic input extension technique is exploited by adding an integrator at the input side and by applying a discontinuous distributed input to the integrator we present a constructive lyapunov analysis of the closed loop performance that yields simple controller tuning conditions guaranteeing the asymptotic tracking of a sufficiently smooth reference trajectory despite the presence of norm bounded persistent disturbances numerical simulations confirm the effectiveness of the proposed approach

direct solve of electrically large integral equations for problem sizes to 1 m unknowns when unknowns are spatially grouped for electrically large bodies the blocked method of moments mom z matrix and its lu factors are comprised of blocks which can be well approximated by matrices of low rank expressed as the outer product of a column matrix times a row matrix this approximation is called matrix compression and can save significant memory and operations count and for monostatic scattering where there are many right hand sides rhs for electrically large bodies the blocked rhs v and current solution j are also well approximated by this low rank outer product form the blocked system equation zj luj v is lu factored and solved using this compressed block form where each outer product approximant is computed using the adaptive cross approximation aca this approach has been applied to a frequency domain efie rwg galerkin integral equation for 3 d pec surfaces preliminary results for this compressed block lu factor and solve technique are presented and compared to measured data bor code predictions and the same code without matrix compression complexity of this approach is studied numerically for an open pipe geometry with specific error tolerances using a pc workstation with unknowns n ranging from 2592 to 1 025 109 and the number of rhs varying from 310 to 6162 matrix fill time scales as n1 34 lu matrix memory storage scales as n1 5 lu factor time scales as n2 0 and the time per rhs solve scales as n1 67 complete solution wall time scales as n1 8

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

fast direct solution of method of moments linear system a novel algorithm the compressed block decomposition cbd is presented for highly accelerated direct noniterative method of moments mom solution of electromagnetic scattering and radiation problems the algorithm is based on a block wise subdivision of the mom impedance matrix impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly but approximated in a compressed form subsequently the matrix is decomposed preserving the compression examples are presented of typical problems in the range of 5000 to 70000 unknowns the total execution time for the largest problem is about 1 h and 20 min for a single excitation vector the main strength of the method is for problems with multiple excitation vectors monostatic rcs computations due to the negligible extra cost for each new excitation for radiation and scattering problems in free space the numerical complexity of the algorithm is shown to be n 2 and the storage requirements scale with n 3 2

a k 1 slope theorem for the k dimensional infinite group relaxation we prove that any minimal valid function for the k dimensional innite group relaxation that is piecewise linear with at most k 1 slopes and does not factor through a linear map with non trivial kernel is extreme this generalizes a theorem of gomory and johnson for k 1 and cornu ejols and molinaro for k 2

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

tracking control of the uncertain heat and wave equation via power fractional and sliding mode techniques in the present paper preliminary results towards the generalization to the infinite dimensional setting of some well known robust finite dimensional control algorithms are illustrated more specifically we deal with the tracking problem for some classes of linear uncertain infinite dimensional systems evolving in hilbert spaces we design distributed variable structure stabilizers that are shown to be effective in the presence of external disturbances the main focus of the present paper is on the rejection of nonvanishing external disturbances the generalization to the infinite dimensional setting of the well known finite dimensional controllers namely the power fractional controller s p bhat and d s bernstein siam j control optim 38 2000 pp 751 766 and two second order sliding mode control algorithms the twisting and supertwisting algorithms l fridman and a levant higher order sliding modes as a natural phenomenon in control theory in robust control via variable structure and lyapunov techniques springer verlag berlin 1996 pp 107 133 a levant internat j control 58 1993 pp 1247 1263 is the main contribution of the present investigation first the distributed twisting control algorithm is developed to address the asymptotic state tracking of the perturbed wave equation next the finite time state tracking of the unperturbed heat equation is provided by means of a distributed power fractional controller finally the distributed supertwisting controller is suggested to address the asymptotic state tracking of the heat equation in spite of the presence of persistent disturbances constructive proofs of stability are developed via the lyapunov functional technique which leads to simple tuning rules for the controller parameters simulation results are discussed to verify the effectiveness of the proposed schemes

error analysis for matrix factorizations using non overlapped localizing basis functions local global solution logos modes provide a computationally efficient framework for developing error controllable fast direct solution methods for electromagnetic simulations this communication provides an error control analysis for the non overlapped localizing logos factorization procedure the error analysis indicates how to control the error in the factored representation of the system matrix numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of pec scattering problems while maintaining the efficiency of the logos factorization

a sliding mode observer for a linear reaction convection diffusion equation with disturbances abstract a sliding mode observer is designed and analyzed for a linear reaction convection diffusion equation subject to external disturbances based on a discontinuous input the proposed observer ensures both state estimation and disturbance rejection using only one boundary measurement an appropriate lyapunov function is used to prove the asymptotic convergence of the observation error the performance of the proposed observer is illustrated by some numerical simulation results

exponential stabilization of conservation systems with interior disturbance abstract in this paper we consider the stabilization problem of the conservation systems with interior disturbance employing the idea of sliding mode control we design a nonlinear distributed feedback controller we prove the solvability of the resulted closed loop system by the maximal monotone operator theory further we prove the exponential stability of the closed loop system in particular we prove that the requirement of a classical solution in the lyapunov approach is unnecessary

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

worst case comparison of valid inequalities for the tsp we consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst case improvement resulting from their addition to the subtour polyhedron for example we show that the comb inequalities cannot improve the subtour bound by a factor greater than 10 9 the corresponding factor for the class of clique tree inequalities is 8 7 while it is 4 3 for the path configuration inequalities

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

study of mixed order basis functions for the locally corrected nystro spl uml m method a high order locally corrected nystro spl uml m lcn method employing the mixed order basis functions proposed by c 80al spl iota s 80kan and peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies an integral operator based on a combined field formulation for conducting surfaces and a mu spl uml ller formulation for dielectric surfaces is used it is found that for general scattering objects mixed order basis functions accelerate the convergence of the lcn solution can eliminate spurious charges and can significantly reduce the condition number of the impedance matrix

a dual field domain decomposition method for the time domain finite element analysis of large finite arrays a novel dual field time domain finite element domain decomposition method is presented for an efficient and broadband numerical simulation of electromagnetic properties of large finite arrays instead of treating the entire array as a single computation domain the method considers each array element as a smaller subdomain and computes both the electric and magnetic fields inside each subdomain adjacent subdomains are related to each other by the equivalent surface currents on the subdomain interfaces in an explicit manner furthermore the method exploits the identical geometry of the array elements and further reduces the memory requirement and cpu time the proposed method is highly efficient for the simulation of large finite arrays numerical stability and computational performance of the method are discussed several radiation examples are presented to demonstrate the accuracy and efficiency of the method

sparse representation for color image restoration sparse representations of signals have drawn considerable interest in recent years the assumption that natural signals such as images admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data in particular the design of well adapted dictionaries for images has been a major challenge the k svd has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks in this paper we address the problem of learning dictionaries for color images and extend the k svd based grayscale image denoising algorithm that appears in this work puts forward ways for handling nonhomogeneous noise and missing information paving the way to state of the art results in applications such as color image denoising demosaicing and inpainting as demonstrated in this paper

equivalence principle algorithm with body of revolution equivalence surface for the modeling of large multiscale structures we propose a multiscale solver of equivalence principle algorithm with a body of revolution bor equivalence surface es first the whole object is decomposed into subdomains the ess are defined as proper bors e g spheres in this work to enclose each subdomain the rao wilton glisson rwg and bor basis functions are defined on each sphere respectively second the octree is constructed in each nonzero subdomain the multilevel fast multipole algorithm mlfma is employed to solve the equivalent currents on the es individually and then the equivalent currents are projected from rwg onto the bor basis functions the couplings between neighboring subdomains are evaluated directly using mlfma and the separated subdomains are substituted by the es to es couplings and are evaluated efficiently by the bor method of moments bor mom to solve the equation system a hybrid inner and outer iterative solver is employed where the inner iteration is used to solve each local subdomains and the outer iteration is used to update the global solutions by collecting all the local solutions numerical results and discussions demonstrate the validity of the proposed work

exponential stabilization of the uncertain wave equation via distributed dynamic input extension the wave equation is studied under the effect of a persistent external perturbation a dynamical distributed controller is suggested based on an infinite dimensional generalization of second order sliding mode control techniques that provides the exponential attainment of a sufficiently smooth arbitrary reference of the state trajectory the control system comprises of both feedforward and feedback parts the latter being a discontinuous term directly connected to the plant input through a dynamical filter that augments the system state smoothing out the discontinuity of the feedback control loop as a result a continuous input is applied to the plant a constructive lyapunov based proof of convergence of the proposed control algorithm is carried out and supporting numerical results are presented

discretization of hybrid vsie using mixed mesh elements with zeroth order galerkin basis functions the hybrid volume and surface integral equation approach is applied to solve electromagnetic scattering and radiation problems involving conducting and or dielectric objects to flexibly and accurately model the complex structures and reduce the number of unknowns mixed mesh scheme is developed to discretize the object in this scheme the triangles and quadrangles are used to discretize the conducting part of the object and the tetrahedrons hexahedrons prisms and pyramids are used to model the dielectric volumes of the scatterer numerical results showed the solution accuracies from the mixed element meshes are of the same level compared with the single element meshes but uses much less number of unknowns this leads to flexibility for mesh generating and reduces the use of computing resources

brief paper sliding mode boundary control of a parabolic pde system with parameter variations and boundary uncertainties this paper considers the stabilization problem of a one dimensional unstable heat conduction system rod modeled by a parabolic partial differential equation pde powered with a dirichlet type actuator from one of the boundaries by applying the volterra integral transformation a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties the associated lyapunov function is used for designing an infinite dimensional sliding manifold on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances it is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero a continuous control law satisfying the reaching condition is obtained by passing a discontinuous signum signal through an integrator

iterative sparsification projection fast and robust sparse signal approximation in this paper we address recovery of sparse signals from compressed measurements and sparse signal approximation which have received considerable attention over the last decade first we revisit smoothed l0 sl0 a well known sparse recovery algorithm and give some insights into it that have not been noticed previously specifically we re derive the sl0 algorithm based on proximal methods and using recent results in solving nonconvex problems by proximal algorithms we provide a convergence guarantee for it in addition inspired by this derivation we propose a general family of algorithms which we call iterative sparsification projection isp having sl0 as a special member our algorithmic framework starts with an initial guess for the unknown sparse vector and then iteratively sparsifies it using a fixed threshold followed by projecting the result onto the admissible solution set the threshold is then decreased and the same process is repeated the algorithm terminates when the threshold becomes sufficiently small or another stopping criterion is satisfied we also propose a robust projection to handle the situations with observation noise or model uncertainties our extensive simulations confirm the promising performance of the isp algorithms compared with some well known algorithms

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

generalized mixed integer rounding inequalities facets for infinite group polyhedra we present a generalization of the mixed integer rounding mir approach for generating valid inequalities for mixed integer programming mip problems for any positive integer n we develop n facets for a certain n 1 dimensional single constraint polyhedron in a sequential manner we then show that for any n the last of these facets which we call the n step mir facet can be used to generate a family of valid inequalities for the feasible set of a general mixed ip constraint which we refer to as the n step mir inequalities the gomory mixed integer cut and the 2 step mir inequality of dash and gunluk math program 105 1 29 53 2006 are the first two families corresponding to n 1 2 respectively the n step mir inequalities are easily produced using periodic functions which we refer to as the n step mir functions none of these functions dominates the other on its whole period finally we prove that the n step mir inequalities generate two slope facets for the infinite group polyhedra and hence are potentially strong

sparse pseudo inverse of the discrete plane wave transform an algorithm is presented for the sparse pseudo inversion of discrete forms of the plane wave transform the starting point for the sparse pseudo inverse is a new sparse representation of the discrete plane wave transform dpwt while other sparse representations of the dpwt exist the sparse representation developed here is shown to be amenable to sparse factorization this feature is used to develop an efficient error controlled pseudo inverse of the dpwt representative numerical examples are provided to illustrate the general properties of the proposed algorithms areas for additional work are identified and potential applications of the results are discussed

t space and cutting planes in this paper we show how knowledge about t space translates directly into cutting planes for general integer programming problems after providing background on corner polyhedra and on t space this paper examines t space in some detail it gives a variety of constructions for t space facets all of which translate into cutting planes and introduces continuous families of facets in view of the great variety of possible facets no one of which can be dominated either by any other or by any combination of the others a measure of merit is introduced to provide guidance on their usefulness t spaces based on higher dimensional groups are discussed briefly as is the idea of going beyond cutting planes to iterated approximations of corner polyhedra

lq optimal control of hyperbolic pdaes the linear quadratic control synthesis for a set of coupled first order hyperbolic partial differential and algebraic equations is presented by using the infinite dimensional hilbert state space representation of the system and the well known operator riccati equation ore method solving the algebraic equations and substituting them into the partial differential equations pdes results in a model consisting of a set of pure hyperbolic pdes the resulting pde system involves a hyperbolic operator in which the velocity matrix is spatially varying non symmetric and its eigenvalues are not necessarily negative through of the domain the c0 semigroup generation property of such an operator is proven and it is shown that the generated c0 semigroup is exponentially stable and consequently the ore has a unique and non negative solution conversion of the ore into a matrix riccati differential equation allows the use of a numerical scheme to solve the control problem

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

the worst case analysis of strong knapsack facets in this paper we identify strong facet defining inequalities for the master knapsack polytope our computational experiments for small master knapsack problems show that 1 k facets for small values of k k le 4 k 4 are strong facets for the knapsack polytope we show that this finding is robust by proving that the removal of these facets from the master knapsack polytope significantly weakens the resulting relaxation in the worst case we show that the 1 k facets for k 1 k 1 are the strongest in that their removal from the master knapsack polytope weakens the relaxation by a factor of 3 2 in the worst case we then show that the 1 k facets with k 3 k 3 or 4 are the next strongest we also show that the strength of the 1 k facets weakens as k grows and that the 1 k facets with k even are stronger than the 1 k facets with k odd

an analysis and design method for uncertain variable structure systems with bounded controllers we present a method for estimating the asymptotic stability region asr of uncertain variable structure systems with bounded switching feedback controllers using linear matrix inequalities lmis we estimate the asr and we show the exponential stability of the closed loop control system in the estimated asr we also give a simple lmi based method for designing switching surfaces that will make the estimated asr big finally we give numerical examples in order to show the effectiveness of our method

comparing measures of sparsity sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation compression sampling and signal analysis the aim of this paper is to compare several commonly used sparsity measures based on intuitive attributes intuitively a sparse representation is one in which a small number of coefficients contain a large proportion of the energy in this paper six properties are discussed robin hood scaling rising tide cloning bill gates and babies each of which a sparsity measure should have the main contributions of this paper are the proofs and the associated summary table which classify commonly used sparsity measures based on whether or not they satisfy these six propositions only two of these measures satisfy all six the pq mean with p les 1 q 1 and the gini index

corner polyhedra and their connection with cutting planes we review the necessary background on corner polyhedra and use this to show how knowledge about corner polyhedra and subadditive functions translates into a great variety of cutting planes for general integer programming problems experiments are described that indicate the dominance of a relatively small number of the facets of corner polyhedra this has implications for their value as cutting planes

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

boundary second order sliding mode control of an uncertain heat process with unbounded matched perturbation the primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation the underlying heat process is governed by an uncertain parabolic partial differential equation pde with neumann boundary conditions it exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance which is not available for measurements and which is possibly unbounded in magnitude the proposed robust synthesis is formed by the linear feedback design and by the twisting second order sliding mode control algorithm suitably combined and re worked in the infinite dimensional setting a non standard lyapunov functional is invoked to establish the global asymptotic stability in a sobolev space involving spatial state derivatives of the same order as that of the plant equation the stability proof is accompanied by a set of simple tuning rules for the controller parameters the effectiveness of the developed control scheme is supported by simulation results

recursive algorithms for calculating the scattering from n strips or patches using the definition of recursive relations for the reflection operator for n strips or patches two easily programmable recursive algorithms are developed to calculate the electromagnetic scattering by n strips or patches one algorithm is for arbitrary excitation and the other is for a fixed excitation the recursive algorithms require the inversion of small matrices at each stage and hence are suitable for programming on smaller computers if the n strips or patches are identical and equally spaced symmetry can be exploited to speed up the algorithms a program was developed to calculate scattering by n strips and the result is shown to converge to scattering by a large strip when the n strips are contiguous

fast sparse approximation for least squares support vector machine in this paper we present two fast sparse approximation schemes for least squares support vector machine ls svm named fsals svm and pfsals svm to overcome the limitation of ls svm that it is not applicable to large data sets and to improve test speed fsals svm iteratively builds the decision function by adding one basis function from a kernel based dictionary at one time the process is terminated by using a flexible and stable epsilon insensitive stopping criterion a probabilistic speedup scheme is employed to further improve the speed of fsals svm and the resulting classifier is named pfsals svm our algorithms are of two compelling features low complexity and sparse solution experiments on benchmark data sets show that our algorithms obtain sparse classifiers at a rather low cost without sacrificing the generalization performance

blind separation of time position varying mixtures we address the challenging open problem of blindly separating time position varying mixtures and attempt to separate the sources from such mixtures without having prior information about the sources or the mixing system unlike studies concerning instantaneous or convolutive mixtures we assume that the mixing system medium is varying in time position attempts to solve this problem have mostly utilized so far online algorithms based on tracking the mixing system by methods previously developed for the instantaneous or convolutive mixtures in contrast with these attempts we develop a unified approach in the form of staged sparse component analysis ssca accordingly we assume that the sources are either sparse or can be sparsified in the first stage we estimate the filters of the mixing system based on the scatter plot of the sparse mixtures data using a proper clustering and curve surface fitting in the second stage the mixing system is inverted yielding the estimated sources we use the ssca approach for solving three types of mixtures time position varying instantaneous mixtures single path mixtures and multipath mixtures real life scenarios and simulated mixtures are used to demonstrate the performance of our approach

a sparse factorization for fast computation of localizing modes localizing modes provide an effective basis for developing efficient error controlled factorizations of the dense matrices encountered in integral equation formulations of wave phenomena at low to moderate frequencies an essential component of these factorization algorithms is the numerical determination of the underlying localizing modes this communication describes the details of an efficient procedure for computing the so called non overlapping localizing modes the principle component of the procedure is a qr like factorization of the sparse multilevel data structure used to compress discrete integral operators numerical examples demonstrate the performance of the algorithm

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

rate distortion behavior of sparse sources the rate distortion behavior of sparse memoryless sources is studied these serve as models of sparse signal representations and facilitate the performance analysis of sparsifying transforms like the wavelet transform and nonlinear approximation schemes for strictly sparse binary sources with hamming distortion r d is shown to be almost linear for nonstrictly sparse continuous valued sources termed compressible two measures of compressibility are introduced incomplete moments and geometric mean the former lead to low and high rate upper bounds on mean squared error d r while the latter yields lower and upper bounds on source entropy thereby characterizing asymptotic r d behavior thus the notion of compressibility is quantitatively connected with actual lossy compression these bounding techniques are applied to two source models gaussian mixtures and power laws matching the approximately scale invariant decay of wavelet coefficients the former are versatile models for sparse data which in particular allow to bound high rate compression performance of a scalar mixture compared to a corresponding unmixed transform coding system such a comparison is interesting for transforms with known coefficient decay but unknown coefficient ordering e g when positions of highest variance coefficients are unknown the use of these models and results in distributed coding and compressed sensing scenarios are also discussed

sliding mode boundary control of an euler bernoulli beam subject to disturbances in this paper a control technique is presented for an undamped pinned pinned euler bernoulli beam with control inputs and bounded disturbances on one boundary the control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances this is achieved in two main steps first a backstepping transformation is used to convert the marginally stable euler bernoulli beam system to a new form that has an exponentially stable homogeneous form control inputs are needed to fully convert the system to this form however since they are distorted by unknown bounded disturbances the next step implements a sliding mode controller to account for them the proposed sliding manifolds require a combination of classical and second order techniques in order to avoid discontinuous chattering on the physical system therefore the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate and do so in the presence of unknown bounded disturbances on the boundary the main contributions of this paper with respect to previous backstepping designs for the euler bernoulli beam are that all three of the following goals are accomplished together i steady state position is the origin ii decay rate has no theoretical restrictions and iii is robust to bounded disturbances

deep neural network predicts emotional responses of the human brain from functional magnetic resonance imaging abstract an artificial neural network with multiple hidden layers known as a deep neural network or dnn was employed as a predictive model dnnp for the first time to predict emotional responses using whole brain functional magnetic resonance imaging fmri data from individual subjects during fmri data acquisition 10 healthy participants listened to 80 international affective digital sound stimuli and rated their own emotions generated by each sound stimulus in terms of the arousal dominance and valence dimensions the whole brain spatial patterns from a general linear model i e beta valued maps for each sound stimulus and the emotional response ratings were used as the input and output for the dnnp respectively based on a nested five fold cross validation scheme the paired input and output data were divided into training three fold validation one fold and test one fold data the dnnp was trained and optimized using the training and validation data and was tested using the test data the pearson s correlation coefficients between the rated and predicted emotional responses from our dnnp model with weight sparsity optimization mean standard error 0 52 0 02 for arousal 0 51 0 03 for dominance and 0 51 0 03 for valence with an input denoising level of 0 3 and a mini batch size of 1 were significantly greater than those of dnn models with conventional regularization schemes including elastic net regularization 0 15 0 05 0 15 0 06 and 0 21 0 04 for arousal dominance and valence respectively those of shallow models including logistic regression 0 11 0 04 0 10 0 05 and 0 17 0 04 for arousal dominance and valence respectively average of logistic regression and sparse logistic regression and those of support vector machine based predictive models svmps 0 12 0 06 0 06 0 06 and 0 10 0 06 for arousal dominance and valence respectively average of linear and non linear svmps this difference was confirmed to be significant with a bonferroni corrected p value of less than 0 001 from a one way analysis of variance anova and subsequent paired t test the weights of the trained dnnps were interpreted and input patterns that maximized or minimized the output of the dnnps i e the emotional responses were estimated based on a binary classification of each emotion category e g high arousal vs low arousal the error rates for the dnnp 31 2 1 3 for arousal 29 0 1 7 for dominance and 28 6 3 0 for valence were significantly lower than those for the linear svmp 44 7 2 0 50 7 1 7 and 47 4 1 9 for arousal dominance and valence respectively and the non linear svmp 48 8 2 3 52 2 1 9 and 46 4 1 3 for arousal dominance and valence respectively as confirmed by the bonferroni corrected p

groupwise elastic registration by a new sparsity promoting metric application to the alignment of cardiac magnetic resonance perfusion images this paper proposes a methodology for the joint alignment of a sequence of images based on a groupwise registration procedure by using a new family of metrics that exploit the expected sparseness of the temporal intensity curves corresponding to the aligned points therefore this methodology is able to tackle the alignment of temporal sequences of images in which the represented phenomenon varies in time specifically we have applied it to the correction of motion in contrast enhanced first pass perfusion cardiac magnetic resonance images the time sequence is elastically registered as a whole by using the aforementioned family of multi image metrics and jointly optimizing the parameters of the transformations involved the proposed metrics are able to cope with dynamic changes in the intensity content of corresponding points in the sequence guided by the assumption that these changes allow for a sparse representation in a properly selected frame results have shown the statistically significant improvement in the performance of the proposed metric with respect to previous groupwise registration metrics for the problem at hand which is especially relevant to correct for elastic deformations

modular fast direct electromagnetic analysis using local global solution modes local global solution logos modes provide a computationally efficient framework for developing fast direct solution methods for electromagnetic simulations logos modes provide a single basis for which both electromagnetic operators and their inverses are sparse with a controllable accuracy for fixed frequency modeling with h refinement efficient application of this observation is shown to provide efficient factorization algorithms for both integral equation and finite element methods in addition to providing fast direct solutions the logos framework is also shown to provide a new strategy for modular electromagnetic analysis the possibility of developing efficient direct solution strategies at high frequencies using the logos framework is also discussed

a dictionary learning approach for poisson image deblurring the restoration of images corrupted by blur and poisson noise is a key issue in medical and biological image processing while most existing methods are based on variational models generally derived from a maximum a posteriori map formulation recently sparse representations of images have shown to be efficient approaches for image recovery following this idea we propose in this paper a model containing three terms a patch based sparse representation prior over a learned dictionary the pixel based total variation regularization term and a data fidelity term capturing the statistics of poisson noise the resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting extensive experimental results suggest that in terms of visual quality peak signal to noise ratio value and the method noise the proposed algorithm outperforms state of the art methods

a parallel finite element tearing and interconnecting algorithm for solution of the vector wave equation with pml absorbing medium a domain decomposition method based on the finite element tearing and interconnecting feti algorithm is presented for the solution of the large sparse matrices associated with the finite element method fem solution of the vector wave equation the feti algorithm is based on the method of lagrange multipliers and leads to a reduced order system which is solved using the biconjugate gradient method bicgm it is shown that this method is highly scalable and is more efficient on parallel platforms when solving large matrices than traditional iterative methods such as a preconditioned conjugate gradient algorithm this is especially true when a perfectly matched layer pml absorbing medium is used to terminate the problem domain

exponential wavelet iterative shrinkage thresholding algorithm for compressed sensing magnetic resonance imaging it is beneficial for both hospitals and patients to accelerate mri scanning recently a new fast mri technique based on cs was proposed however the reconstruction quality and computation time of cs mri did not meet the standard of clinical use therefore we proposed a novel algorithm based on three successful components the sparsity of ewt the rapidness of fista and the excellent tuning in sista the proposed method was dubbed exponential wavelet iterative shrinkage threshold algorithm ewista experiments over four kinds of mr images brain ankle knee and adhd indicated that the proposed ewista showed better reconstruction performance than the state of the art algorithms such as fcsa ista fista sista and ewt ista moreover ewista was faster than ista and ewt ista but slightly slower than fcsa fista and sista