hp dgfem for second order elliptic problems in polyhedra ii exponential convergence the goal of this paper is to establish exponential convergence of hp version interior penalty ip discontinuous galerkin dg finite element methods for the numerical approximation of linear second order elliptic boundary value problems with homogeneous dirichlet boundary conditions and piecewise analytic data in three dimensional polyhedral domains more precisely we shall analyze the convergence of the hp ip dg methods considered in d schotzau c schwab t p wihler siam j numer anal 51 2013 pp 1610 1633 based on axiparallel sigma geometric anisotropic meshes and bm s linear anisotropic polynomial degree distributions

rank revealing qr factorizations abstract an algorithm is presented for computing a column permutation pi and a qr factorization a pi qr of an m by n m or n matrix a such that a possible rank deficiency of a will be revealed in the triangular factor r having a small lower right block for low rank deficient matrices the algorithm is guaranteed to reveal the rank of a and the cost is only slightly more than the cost of one regular qr factorization a posteriori upper and lower bounds on the singular values of a are derived and can be used to infer the numerical rank of a keywords qr factorization rank deficient matrices least squares computation subset selection rank singular values

periodic van der pol equation with state dependent impulses abstract conditions are given for the existence of a solution of given period to the impulsively driven van der pol equation results are obtained for impulses of varying degrees of state dependence

filtering and frequency estimation using perturbation formulas a new method for updating the svd is introduced based on perturbation formulas the complexity of the method is o n sup 2 applications are made to frequency estimation and filtering

nonresonance impulsive functional differential inclusions with variable times in this paper we investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions with variable moments the proofs make use of the martelli fixed point theorem for condensing multivalued maps

urv esprit for tracking time varying signals esprit is an algorithm for determining the fixed directions of arrival of a set of narrowband signals at an array of sensors unfortunately its computational burden makes it unsuitable for real time processing of signals with time varying directions of arrival the authors develop a new implementation of esprit that has potential for real time processing it is based on a rank revealing urv decomposition rather than the eigendecomposition or singular value decomposition used in previous esprit algorithms the authors demonstrate its performance on simulated data representing both constant and time varying signals they find that the urv based esprit algorithm is effective for estimating time varying directions of arrival at considerable computational savings over the svd based algorithm

periodic duffing delay equations with state dependent impulses conditions are obtained for the duffing equation with delay and state dependent impulses to admit a periodic solution

a systolic implementation of the chan foster rrqr algorithm the rank revealing qr factorization is a useful tool in many signal processing applications since it explicitly yields all the necessary information to solve rank deficient least squares problems and subset selection problems to compute signal and noise subspaces etc the authors present a systolic algorithm for computing a rank revealing qr factorization and consider the performance of the algorithm

improved bound for rank revealing lu factorizations abstract in many applications it is necessary to determine the rank or numerical rank of a matrix many of these situations involve matrices that are very large order or that are sparse or that may undergo some form of modification rank k update row or column appended or removed in these cases the singular value decomposition s cost may be prohibitively high or the decomposition may not be computationally feasible especially for large sparse problems we thus examine the theoretical merits of rank revealing lu rrlu factorizations we find that in those cases where the nullity is small and the gap is well defined an rrlu factorization could be a very useful tool

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

bi iterative least square method for subspace tracking subspace tracking is an adaptive signal processing technique useful for a variety of applications in this paper we introduce a simple bi iterative least square bi ls method which is in contrast to the bi iterative singular value decomposition bi svd method we show that for subspace tracking the bi ls method is easier to simplify than the bi svd method the linear complexity algorithms based on bi ls are computationally more efficient than the existing linear complexity algorithms based on bi svd although both have the same performance for subspace tracking a number of other existing subspace tracking algorithms of similar complexity are also compared with the bi ls algorithms

rounding errors in solving block hessenberg systems a rounding error analysis is presented for a divide and conquer algorithm to solve linear systems with block hessenberg matrices conditions are derived under which the algorithm computes a stable solution the algorithm is shown to be stable for block diagonally dominant matrices and for m matrices

fast low rank modifications of the thin singular value decomposition this paper develops an identity for additive modivations of a singular value decomposition svd to reflect updates downdates shifts and edits of the data matrix this sets the stage for fast and ememory efficient sequential algorithms for tracking singular values and subspaces in conjunction with a fast solution for the pseudo inverse of a submatrix of an orthogonal matrix we develop a scheme for computing a thin svd of streaming data in a single pass with linear time complexity a rank r think svd of a p x q matrix can be computed in o pqr time for r less than or equal sqroot min p q linear algebra and its applications

positive periodic solutions of functional differential equations with impulses and a parameter by applying the well known leggett williams multiple fixed point theorem this paper investigates the existence of multiple positive periodic solutions of functional differential equations with impulses and a parameter

exponential convergence of mixed hp dgfem for stokes flow in polygons we analyze mixed hp discontinuous galerkin finite element methods dgfem for stokes flow in polygonal domains in conjunction with geometrically refined quadrilateral meshes and linearly increasing approximation orders we prove that the hp dgfem leads to exponential rates of convergence for piecewise analytic solutions exhibiting singularities near corners

conjugate gradient eigenstructure tracking for adaptive spectral estimation a conjugate gradient iteration is derived that converges to the set of r dominant subdominant eigenpairs this iteration is used to construct two eigenstructure tracking algorithms that track the r dimensional dominant or subdominant subspaces of time varying data or data covariance matrices the two eigenstructure tracking algorithms have update complexities o m sup 2 r and the other o mr sup 2 where m is the data dimension the algorithms are customized to solve high resolution temporal and spatial frequency tracking problems they are compared with existing techniques by tying into published simulation based performance tests the algorithms demonstrate rapid convergence and tracking characteristics at a competitive cost

exponential convergence of the hp dgfem for diffusion problems abstract we prove exponential convergence of the hp version of discontinuous galerkin fem on geometrically refined meshes in polygons several variants of interior penalization are covered numerical experiments indicate the sharpness of the theoretical results as well as the weak dependence of the dgfem approximation on the particular choice of interior penalization and the penalty parameter

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

recursive blind symbol estimation of convolutionally coded cochannel signals a recursive blind equalizer is presented that directly estimates the transmitted symbols of multiple cochannel signals in the presence of isi the algorithm exploits shift structure present in the data model and the finite alphabet property of the signals the proposed method possesses a separation property that allows the symbol sequences for each user to be estimated independently of the others problematic issues surrounding unknown and mismatched channel lengths for the cochannel users can be handled effectively in the recursive equalizer additionally if the cochannel signals are encoded prior to transmission we show how the code structure can be incorporated into the recursive equalizer to improve its performance

stabilized hp finite element methods for first order hyperbolic problems we analyze the hp version of the streamline diffusion finite element method sdfem and of the discontinuous galerkin finite element method dgfem for first order linear hyperbolic problems for both methods we derive new error estimates on general finite element meshes which are sharp in the mesh width h and in the spectral order p of the method assuming that the stabilization parameter is o h p for piecewise analytic solutions exponential convergence is established on quadrilateral meshes for the dgfem we admit very general irregular meshes and for the sdfem we allow meshes which contain hanging nodes numerical experiments confirm the theoretical results

an optimal order error estimate for the discontinuous galerkin method in this paper a new approach is developed for analyzing the discontinuous galerkin method for hyperbolic equations for a model problem in r2 the method is shown to converge at a rate 0 hn l when applied with nth degree polynomial approxi mations over a semiuniform triangulation assuming sufficient regularity in the solution

on the stability of sequential updates and downdates the updating and downdating of cholesky decompositions has important applications in a number of areas there is essentially one standard updating algorithm based on plane rotations which is backward stable three downdating algorithms have been treated in the literature the linpack algorithm the method of hyperbolic transformations and chambers 1971 algorithm although none of these algorithms is backward stable the first and third satisfy a relational stability condition it is shown that relational stability extends to a sequence of updates and downdates in consequence other things being equal if the final decomposition in the sequence is well conditioned it will be accurately computed even though intermediate decompositions may be almost completely inaccurate these results are also applied to the two sided orthogonal decompositions such as the urv decomposition

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

blind adaptive multiuser detection in multipath cdma channels based on subspace tracking a blind adaptive technique for signal demodulation in multipath code division multiple access cdma communication channels is proposed this technique is based on signal subspace estimation the receiver employs a bank of linear filters decorrelating filters or linear mmse filters at the front end to mitigate the multiple access interference and the multipath interference a channel estimator is used to estimate the channel state for diversity combining it is shown that through the use of signal subspace estimation both the decorrelating filterbank and the linear mmse filterbank can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform of the desired user two forms of the subspace based linear filterbanks are developed and their equivalence in terms of the interference suppression capability is established these subspace based blind adaptive interference suppression techniques require at each symbol epoch the eigenvalues and the eigenvectors of an appropriate signal subspace which ran be obtained using computationally efficient sequential adaptive eigendecomposition subspace tracking algorithms moreover a blind adaptive method for estimating the channel state is developed which also produces the postcombining decision statistic as a byproduct

a krylov multisplitting algorithm for solving linear systems of equations abstract we consider the practical implementation of krylov subspace methods conjugate gradients gmres etc for parallel computers in the case where the preconditioning matrix arises from a multisplitting we show that the algorithm can be efficiently implemented by dividing the work into tasks that generate search directions and a single task that minimizes over the resulting subspace each task is assigned to a subset of processors it is not necessary for the minimization task to send frequent information to the direction generating tasks and this leads to high utilization with a minimum of synchronization we study the convergence properties of various forms of the algorithm and present results of numerical examples on a sequential computer

discontinuous galerkin finite element approximation of hamilton jacobi bellman equations with cordes coefficients we propose an hp version discontinuous galerkin finite element method for fully nonlinear second order elliptic hamilton jacobi bellman equations with cordes coefficients the method is proved to be consistent and stable with convergence rates that are optimal with respect to mesh size and suboptimal in the polynomial degree by only half an order numerical experiments on problems with nonsmooth solutions and strongly anisotropic diffusion coefficients illustrate the accuracy and computational efficiency of the scheme an existence and uniqueness result for strong solutions of the fully nonlinear problem and a semismoothness result for the nonlinear operator are also provided

a multilevel preconditioner for the interior penalty discontinuous galerkin method in this article we present a multilevel preconditioner for interior penalty discontinuous galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution the underlying triangulations are assumed only to be shape regular but may have hanging nodes subject to certain mild grading conditions a key role is played by certain decompositions of the discontinuous trial space into a conforming subspace and a nonconforming subspace that is controlled by the jumps across the edges

ulv and generalized ulv subspace tracking adaptive algorithms traditional adaptive filters assume that the effective rank of the input signal is the same as the input covariance matrix or the filter length n therefore if the input signal lives in a subspace of dimension less than n these filters fail to perform satisfactorily in this paper we present two new algorithms for adapting only in the dominant signal subspace the first of these is a low rank recursive least squares rls algorithm that uses a ulv decomposition stewart 1992 to track and adapt in the signal subspace the second adaptive algorithm is a subspace tracking least mean squares lms algorithm that uses a generalized ulv gulv decomposition developed in this paper to track and adapt in subspaces corresponding to several well conditioned singular value clusters the algorithm also has an improved convergence speed compared with that of the lms algorithm bounds on the quality of subspaces isolated using the gulv decomposition are derived and the performance of the adaptive algorithms are analyzed

efficient solution of the rank deficient linear least squares problem in this paper we present several new fast and reliable algorithms for solving rank deficient linear least squares problems by means of the complete orthogonal decomposition experimental comparison of our algorithms with the existing implementations in lapack on a wide range of platforms shows considerable performance improvements moreover for full rank matrices the performance of the new algorithm is very close to that of the fast method based on qr factorization thus providing a valuable general tool for full rank matrices rank deficient matrices and those matrices with unknown rank

a survey of condition number estimation for triangular matrices we survey and compare a wide variety of techniques for estimating the condition number of a triangular matrix and make recommendations concerning the use of the estimates in applications each of the methods is shown to bound the condition number the bounds can broadly be categorised as upper bounds from matrix theory and lower bounds from heuristic or probabilistic algorithms for each bound we examine by how much at worst it can overestimate or underestimate the condition number numerical experiments are presented in order to illustrate and compare the practical performance of the condition estimators

on a new class of abstract integral equations and applications abstract in this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations

blind equalization and multiuser detection in dispersive cdma channels the problem of blind demodulation of multiuser information symbols in a high rate code division multiple access cdma network in the presence of both multiple access interference mai and intersymbol interference isi is considered the dispersive cdma channel is first cast into a multiple input multiple output mimo signal model framework by applying the theory of blind mimo channel identification and equalization it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users signature waveforms including the desired user s signature waveform although the algorithmic complexity of such an approach is prohibitively high however in practice the signature waveform of the user of interest is always available at the receiver it is shown that by incorporating this knowledge the impulse response of each user s dispersive channel can be identified using a subspace method it is further shown that based on the identified signal subspace parameters and the channel response two linear detectors that are capable of suppressing both mai and isi i e a zero forcing detector and a minimum mean square error mmse detector can be constructed in closed form at almost no extra computational cost data detection can then be furnished by applying these linear detectors obtained blindly to the received signal the major contribution of this paper is the development of these subspace based blind techniques for joint suppression of mai and isi in the dispersive cdma channels

the laurent expansion of pencils that are singular at the origin abstract this paper gives two new proofs of a theorem of langenhop on the laurent expansion of a matrix pencil that is singular at the origin the second based on a decomposition of van dooren leads to a computational algorithm

superconvergence of the local discontinuous galerkin method for elliptic problems on cartesian grids in this paper we present a superconvergence result for the local discontinuous galerkin ldg method for a model elliptic problem on cartesian grids we identify a special numerical flux for which the l2 norm of the gradient and the l2 norm of the potential are of orders k 1 2 and k 1 respectively when tensor product polynomials of degree at most k are used for arbitrary meshes this special ldg method gives only the orders of convergence of k and k 1 2 respectively we present a series of numerical examples which establish the sharpness of our theoretical results

three anti periodic solutions for second order impulsive differential inclusions via nonsmooth critical point theory abstract a nonsmooth version of a three critical point theorem of ricceri due to iannizzotto is used to obtain three anti periodic solutions for a second order impulsive differential inclusions with a perturbed nonlinearity and two parameters

efficient high performance subspace tracking for time domain data this paper describes two new algorithms for tracking the subspace spanned by the principal eigenvectors of the correlation matrix associated with time domain i e time series data the algorithms track the d principal n dimensional eigenvectors of the data covariance matrix with a complexity of o nd sup 2 yet they have performance comparable with algorithms having o n sup 2 d complexity the computation reduction is achieved by exploiting the shift invariance property of temporal data covariance matrices experiments are used to compare our algorithms with other well known approaches of similar and or lower complexity our new algorithms are shown to outperform the subset of the general approaches having the same complexity the new algorithms are useful for applications such as subspace based speech enhancement and low rank adaptive filtering

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

impulsive functional differential equations with variable times in this note a schaefer fixed point theorem is used to investigate the existence of solutions for first order impulsive functional differential equations with variable times

periodic lienard type delay equations with state dependent impulses abstract conditions are obtained for lienard type equations with delay and state dependent impulses to admit an absolutely continuous periodic solution with first derivative of bounded variation and consequently with lebesgue integrable second derivative the results are applied to josephson s equation and the nonconservative forced pendulum equation

a correlation based subspace tracking algorithm stewart 1992 proposed the urv algorithm as a less complex alternative to the svd by forming the cross product of the urv with its transpose a correlation domain decomposition is produced that involves even less computation this cross product rv crv decomposition is the basis for a new subspace tracking technique

local error estimates for a finite element method for hyperbolic and convection diffusion equations local error estimates of near optimal order are derived for a finite element method for hyperbolic and convection dominated convection diffusion equations in a domain omega subset r 2 the method generates in an explicit fashion a continuous piecewise polynomial approximation of degree n geqslant 2 over a triangulation of omega the scheme is shown to propagate disturbances a distance o sqrt h log frac 1 h in the crosswind direction where h is the meshsize the analysis uses test functions which depend only on the crosswind variable it is also shown to be applicable in a parallel fashion to the discontinuous galerkin method thus underscoring the close interrelationship of the two methods

discontinuous galerkin finite element approximation of nondivergence form elliptic equations with cordes coefficients nondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation thus presenting an obstacle to their numerical solution by classical finite element methods we propose a new hp version discontinuous galerkin finite element method for a class of these problems which satisfy the cordes condition it is shown that the method exhibits a convergence rate that is optimal with respect to the mesh size h and suboptimal with respect to the polynomial degree p by only half an order numerical experiments demonstrate the accuracy of the method and illustrate the potential of exponential convergence under hp refinement for problems with discontinuous coefficients and nonsmooth solutions

a posteriori error estimates of hp discontinuous galerkin method for strongly nonlinear elliptic problems abstract in this paper we study the residual based a posteriori error estimates of h p discontinuous galerkin finite element methods for strongly nonlinear elliptic boundary value problems computable upper and lower bounds on the error are derived in a natural mesh dependent energy norm the bounds are explicit in the local mesh size and the local degree of the approximating polynomial numerical experiments are also provided to illustrate the performance of the proposed estimators

global solutions for abstract impulsive differential equations abstract in this paper we study the existence of solutions on the whole of r for a class of impulsive abstract differential equations an application to partial differential equations is presented

unitary esprit how to obtain increased estimation accuracy with a reduced computational burden esprit is a high resolution signal parameter estimation technique based on the translational invariance structure of a sensor array previous esprit algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary the authors present a simple and efficient method to constrain the estimated phase factors to the unit circle if centro symmetric array configurations are used unitary esprit the resulting closed form algorithm has an esprit like structure except for the fact that it is formulated in terms of real valued computations throughout since the dimension of the matrices is not increased this completely real valued algorithm achieves a substantial reduction of the computational complexity furthermore unitary esprit incorporates forward backward averaging leading to an improved performance compared to the standard esprit algorithm especially for correlated source signals like standard esprit unitary esprit offers an inexpensive possibility to reconstruct the impinging wavefronts signal copy these signal estimates are more accurate since unitary esprit improves the underlying signal subspace estimates simulations confirm that even for uncorrelated signals the standard esprit algorithm needs twice the number of snapshots to achieve a precision comparable to that of unitary esprit thus unitary esprit provides increased estimation accuracy with a reduced computational burden

periodic boundary value problem for first order differential equations with impulses at variable times in this paper we show the validity of the method of upper and lower solutions to obtain an existence result for a periodic boundary value problem of first order impulsive differential equations at variable times

dimension reduction in text classification with support vector machines support vector machines svms have been recognized as one of the most successful classification methods for many applications including text classification even though the learning ability and computational complexity of training in support vector machines may be independent of the dimension of the feature space reducing computational complexity is an essential issue to efficiently handle a large number of terms in practical applications of text classification in this paper we adopt novel dimension reduction methods to reduce the dimension of the document vectors dramatically we also introduce decision functions for the centroid based classification algorithm and support vector classifiers to handle the classification problem where a document may belong to multiple classes our substantial experimental results show that with several dimension reduction methods that are designed particularly for clustered data higher efficiency for both training and testing can be achieved without sacrificing prediction accuracy of text classification even when the dimension of the input space is significantly reduced

hp optimal discontinuous galerkin methods for linear elliptic problems the aim of this paper is to overcome the well known lack of p optimality in hp version discontinuous galerkin dg discretizations for the numerical approximation of linear elliptic problems for this purpose we shall present and analyze a class of hp dg methods that is closely related to other dg schemes however combines both p optimal jump penalty as well as lifting stabilization we will prove that the resulting error estimates are optimal with respect to both the local element sizes and polynomial degrees

an a priori error analysis of the local discontinuous galerkin method for elliptic problems in this paper we present the first a priori error analysis for the local discontinuous galerkin ldg method for a model elliptic problem for arbitrary meshes with hanging nodes and elements of various shapes we show that for stabilization parameters of order one the l2 norm of the gradient and the l2 norm of the potential are of order k and k 1 2 respectively when polynomials of total degree at least k are used if stabilization parameters of order h 1 are taken the order of convergence of the potential increases to k 1 the optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

state space system identification approach to radar data processing space time adaptive processing stap algorithms typically consist of a data transformation step to reduce the number of degrees of freedom and a sampling step wherein radar returns from adjacent range bins are used to estimate interference statistics the reduction in the number of degrees of freedom inadequate sample support presence of target in sampled data and range dependence of interference are some of the main reasons for stap performance loss in this paper we present an approach to target detection and localization that mitigates these performance losses using the well known stochastic realization algorithm from system identification theory we first identify a state space model from the radar return data in range pulse domain for a given range bin and then perform detection and localization using the identified state space matrices as interference statistics are not directly computed and since there is no sampling from adjacent range bins this approach is more robust to sample support issues target in training and range dependence of clutter a numerical comparison of the approach with beam space post doppler stap using simulated data is given

anti periodic solutions of lienard equations with state dependent impulses abstract subject to a priori bounds lienard equations with state dependent impulsive forcing are shown to admit a unique absolutely continuous anti periodic solution with first derivative of bounded variation on finite intervals the point wise convergence of a sequence of iterates to the solution is obtained along with a bound for the rate of convergence the results are applied to josephson s and van der pol s equations

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

existence of solutions for semi linear abstract differential equations with not instantaneous impulses in this paper using the theory of analytic semigroup and fractional power of closed operators we study the existence of solutions for a class of semi linear abstract impulsive differential equations with not instantaneous impulses some applications involving partial differential equations with impulses are presented

stable subspace tracking algorithm based on a signed urv decomposition subspace estimation and tracking are of fundamental importance in many signal processing algorithms the class of schur subspace estimators provides a complete parametrization of all principal subspace estimates defined as the column spans of corresponding low rank matrix approximants that lie within a specified 2 norm distance of a given matrix the parametrization is found in terms of a two sided hyperbolic decomposition hyperbolic urv or hurv which can be computed using hyperbolic rotations unfortunately such rotations are commonly associated with numerical instabilities in this paper we present a numerically stable non iterative algorithm to compute the hurv called the signed urv surv algorithm we show that this algorithm implicitly imposes certain constraints on the hurv such that important norm bounds that guarantee stability are satisfied the constraints also restrict the parametrization of the subspace estimate such that it becomes close to the principal subspace provided by the svd which is a special case within this class the complexity of the algorithm is of the same order as that of a qr update updating and downdating are of the same complexity and are both numerically stable surv is proven to provide rank estimates consistent with the svd with the same rank threshold it can replace an svd where only subspace estimation is needed typical applications would e g be the detection of the number of signals in array signal processing and subspace estimation for source separation and interference mitigation such as the first step in music and esprit type algorithms simulation results demonstrate the numerical stability and confirm that this algorithm provides exact rank estimates and good principal subspace estimates as compared to the svd

perturbations and hopf bifurcation of the planar discontinuous dynamical system abstract the objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point a new technique of investigation is presented conditions for existence of the foci and centres are proposed the focus centre problem and hopf bifurcation are considered appropriate examples are given to ilustrate the bifurcation theorem

blind channel estimation for long code multiuser cdma systems in cdma systems with long codes the users signatures change in each bit period impeding the estimation of the time invariant multipath parameters in this paper correlation matching methods are employed to blindly estimate those multipath parameters for given code sequences the output correlation matrix parameterized by the unknown channel coefficients is compared with its instantaneous approximation by minimizing the frobenius norm of the resulting error matrix the channel parameters can be estimated up to a complex scalar ambiguity both batch and adaptive algorithms are derived under the assumption of i i d code sequences identifiability up to a complex scalar ambiguity for each channel is guaranteed and the asymptotic convergence of the proposed algorithm is established furthermore step size selection for the adaptive version is investigated when only the code sequence of the user of interest is available a single user receiver is also derived simulation results verify those claims and provide comparisons with other methods

a constructive approach to boundary value problems with state dependent impulses we investigate the non linear system of ordinary differential equations u t f t u t a e t a b subject to the state dependent impulse condition u t u t u t for t a b such that g t u t 0 and the linear two point boundary condition a u a c u b d here a b f and are given continuous vector functions g is a continuous scalar function a c are constant matrices and d is a constant vector the instants of time t where the jump occurs are determined by the equation g t u t 0 and thus are unknown a priori and essentially depend on the solution u we discuss a reduction technique allowing one to combine the analysis of existence of solutions with an efficient construction of approximate solutions at present according to the authors knowledge no numerical results for boundary value problems with state dependent impulses are available in the literature

finite precision error analysis of qrd rls and star rls adaptive filters the qr decomposition based recursive least squares rls adaptive filtering qrd rls algorithm is suitable for vlsi implementation since it has good numerical properties and can be mapped onto a systolic array a new fine grain pipelinable star rls algorithm was developed the pipelined star rls algorithm pstar rls is useful for high speed applications the stability of qrd rls star rls and pstar rls has been proved but the performance of these algorithms in finite precision arithmetic has not yet been analyzed the authors determine expressions for the degradation in the performance of these algorithms due to finite precision by exploiting the steady state properties of these algorithms simple expressions are obtained that depend only on known parameters this analysis can be used to compare the algorithms and to decide the wordlength to be used in an implementation since floating or fixed point arithmetic representations may be used in practice both representations are considered the results show that the three algorithms have about the same finite precision performance with pstar rls performing better than star rls which does better than qrd rls these algorithms can be implemented with as few as 8 bits for the fractional part depending on the filter size and the forgetting factor used the theoretical expressions are found to be in good agreement with the simulation results

asymptotic behavior of linear impulsive integro differential equations asymptotic equilibria of linear integro differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro differential equations are established a new gronwall bellman type lemma for integro differential inequalities is proved an example is given to demonstrate the validity of one of the results

blind channel identification subspace tracking method without rank estimation subspace ss methods are an effective approach for blind channel identification however these methods also have two major disadvantages 1 they require accurate channel length estimation and or rank estimation of the correlation matrix which is difficult with noisy channels and 2 they require a large amount of computation for the singular value decomposition svd which makes it inconvenient for adaptive implementation although many adaptive subspace tracking algorithms can be applied the computational complexity is still o m sup 3 where m is the data vector length in this paper we introduce new recursive subspace algorithms using ulv updating and successive cancellation techniques the new algorithms do not need to estimate the rank of the correlation matrix furthermore the channel length can be overestimated initially and be recovered at the end by a successive cancellation procedure which leads to more convenient implementations the adaptive algorithm has computations of o m sup 2 in each recursion the new methods can be applied to either the single user or the multiuser cases simulations demonstrate their good performance

a block qr algorithm and the singular value decomposition abstract in this note we consider an iterative algorithm for moving a triangular matrix toward diagonality the algorithm is related to algorithms for refining rank revealing triangular decompositions and in a variant form to the qr algorithm it is shown to converge if there is a sufficient gap in the singular values of the matrix and the analysis provides a new approximation theorem for singular values and singular subspaces

hp version discontinuous galerkin methods for hyperbolic conservation laws abstract the development of hp version discontinuous galerkin methods for hyperbolic conservation laws is presented in this work a priori error estimates are derived for a model class of linear hyperbolic conservation laws these estimates are obtained using a new mesh dependent norm that reflects the dependence of the approximate solution on the local element size and the local order of approximation the results generalize and extend previous results on mesh dependent norms to hp version discontinuous galerkin methods a posteriori error estimates which provide bounds on the actual error are also developed in this work numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution

impulsive neutral functional differential equations with variable times abstract in this paper a fixed point theorem due to schaefer is used to investigate the existence of solutions for first and second order impulsive neutral functional differential equations with variable times

perturbation theory for orthogonal projection methods with applications to least squares and total least squares the stabilized versions of the least squares ls and total least squares tls methods are two examples of orthogonal projection methods commonly used to solve the overdetermined system of linear equations ax b when a is nearly rank deficient in practice when this system represents the noisy version of an exact rank deficient zero residual problem tls usually yields a more accurate estimate of the exact solution however current perturbation theory does not justify the superiority of tls over ls in this paper we establish a model for orthogonal projection methods by reformulating the parameter estimation problem as an equivalent problem of nullspace determination when the method is based on the singular value decomposition of the matrix a b the model specializes to the well known tls method we derive new lower and upper perturbation bounds for orthogonal projection methods in terms of the subspace angle which shows how the perturbation of the approximate nullspace affects the accuracy of the solution in situations where tls is typically used such as in signal processing where the noise free compatible problem is exactly rank deficient our upper bounds suggest that the tls perturbation bound is usually smaller than the one for ls which means that tls is usually more robust than ls under perturbations of all the data also the bounds permit a comparison between the ls and tls solutions as well as for any two competing orthogonal projection methods we include numerical simulations to illustrate our conclusions