an extension of the conjugate residual method to nonsymmetric linear systems the conjugate gradient cg method and the conjugate residual cr method are krylov subspace methods for solving symmetric positive definite linear systems to solve nonsymmetric linear systems the bi conjugate gradient bi cg method has been proposed as an extension of cg bi cg has attractive short term recurrences and it is the basis for the successful variants such as bi cgstab in this paper we extend cr to nonsymmetric linear systems with the aim of finding an alternative basic solver numerical experiments show that the resulting algorithm with short term recurrences often gives smoother convergence behavior than bi cg hence it may take the place of bi cg for the successful variants

multichannel transforms for signal image processing this paper presents a novel approach to the fourier analysis of multichannel time series orthogonal matrix functions are introduced and are used in the definition of multichannel fourier series of continuous time periodic multichannel functions orthogonal transforms are proposed for discrete time multichannel signals as well it is proven that the orthogonal matrix functions are related to unitary transforms e g discrete hartley transform dht walsh hadamard transform which are used for single channel signal transformations the discrete time one dimensional multichannel transforms proposed in this paper are related to two dimensional single channel transforms notably to the discrete fourier transform dft and to the dht therefore fast algorithms for their computation can be easily constructed simulations on the use of discrete multichannel transforms on color image compression have also been performed

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

the fast hartley transform algorithm the fast hartley transform fht is similar to the cooley tukey fast fourier transform fft but performs much faster because it requires only real arithmetic computations compared to the complex arithmetic computations required by the fft through use of the fht discrete cosine transforms dct and discrete fourier transforms dft can be obtained the recursive nature of the fht algorithm derived in this paper enables us to generate the next higher order fht from two identical lower order fht s in practice this recursive relationship offers flexibility in programming different sizes of transforms while the orderly structure of its signal flow graphs indicates an ease of implementation in vlsi

a note on convergence of quasi minimal residual smoothing in this paper we give convergence result on a quasi minimal residual qmr smoothing approach int j comput math 62 1996 249 appl numer math to appear for solving nonsymmetric linear systems

transpose free multiple lanczos and its application in pade approximation a transpose free two sided nonsymmetric lanczos method is developed for multiple starting vectors on both the left and right the method is mathematically equivalent to the two sided methods without look ahead or deflation steps but avoids the use of the transpose of the system matrix the method is applied to the computation of the matrix pade approximation to a linear dynamical system the result is a method which can be labeled transpose free matrix pade via lanczos tfmpvl under certain circumstances tfmpvl will actually reduce the total number of matrix vector products needed it is illustrated with some numerical examples

a simplified and flexible variant of gcrot for solving nonsymmetric linear systems there is a need for flexible iterative solvers that can solve large scale 10 6 unknowns nonsymmetric sparse linear systems to a small tolerance among flexible solvers flexible gmres fgmres is attractive because it minimizes the residual norm over a particular subspace in practice fgmres is often restarted periodically to keep memory and work requirements reasonable however like restarted gmres restarted fgmres can suffer from stagnation this has led us to develop a flexible variant of the krylov linear solver gcrot generalized conjugate residual with inner orthogonalization and outer truncation unlike the original gcrot algorithm the proposed gcrot variant uses a simplified truncation strategy similar to loose gmres lgmres this modification is motivated by numerical experiments that suggest the specific subspace retained in the outer iteration of gcrot is less important than its size the flexible gcrot variant appears to be well suited for advection dominated problems in particular when applied to an adjoint problem from computational aerodynamics the proposed gcrot variant is robust and efficient compared with several popular truncated krylov subspace methods finally a flexible version of lgmres is easily constructed by recognizing algorithmic similarities to gcrot

interpreting idr as a petrov galerkin method the induced dimension reduction idr method of sonneveld and van gijzen siam j sci comput 31 2008 pp 1035 1062 is shown to be a petrov galerkin projection method with a particular choice of left krylov subspaces these left subspaces are rational krylov spaces consequently other methods such as bicgstab and ml s bicgstab which are mathematically equivalent to some versions of idr can also be interpreted as petrov galerkin methods the connection with rational krylov spaces inspired a new version of idr called ritz idr where the poles of the rational function are chosen as certain ritz values experiments are presented illustrating the effectiveness of this new version

three dimensional visco acoustic modeling using a renormalized integral equation iterative solver we present a frequency domain renormalized integral equation formulation for solving a three dimensional visco acoustic medium using an iterative solver upon applying this special renormalization the resulting integral equation operator can be proven to have a contraction property hence solving the linear system of equations using a krylov optimization method will result in a good convergence rate furthermore since the matrix vector multiplication can be done using a fast fourier transform fft technique its operation is of the order of o n log n where n is the size of the discretization grid this technique also allows us to use matrix free implementation hence the memory usage is about o n numerical tests show that the computational time and memory usage of this renormalized integral equation approach can be quite competitive with the frequency domain finite difference iterative solver further the numerical examples demonstrate that it is possible to solve a problem with over 100 million unknowns using an integral equation approach

gabor representation of generalized functions this paper deals with gabor representation of generalized functions by this we mean that a given function is to be expanded in a series involving gabor functions that are located in the points of a given lattice in the time frequency plane we shall mainly consider lattices in which the area of the elementary cells of the lattice equals 1 in 1946 gabor used these expansions for the simultaneous analysis of signals in time and frequency cf 181 gabor stated that the above mentioned expansions exist for every reasonable signal and that the coefficients in the expansion are uniquely determined by the signal this statement is true when interpreted carefully and the aim of this paper is to find out what kind of generalized functions are sufficiently well behaved to allow a development in a gabor series we shall also consider the question of the uniqueness of the coefficients in the expansions as well as questions concerning convergence it turns out that the uniqueness questions can be handled with the aid of the main results of io in particular 2 12 and 2 13 the questions on the existence of expansions are harder to answer and require special care depending on the particular function we consider lpfunctions 1 p 2 in detail and show existence of gabor representation for tempered distribution in general

time domain modeling of electromagnetic diffusion with a frequency domain code we modeled time domain em measurements of induction currents for marine and land applications with a frequency domain code an analysis of the computational complexity of a number of numerical methods shows that frequency domain modeling followed by a fourier transform is an attractive choice if a sufficiently powerful solver is available a recently developed robust multigrid solver meets this requirement an interpolation criterion determined the automatic selection of frequencies the skin depth controlled the construction of the computational grid at each frequency tests of the method against exact solutions for some simple problems and a realistic marine example demonstrate that a limited number of frequencies suffice to provide time domain solutions after piecewise cubic hermite interpolation and a fast fourier transform

minimal residual smoothing in multi level iterative method a minimal residual smoothing mrs technique is employed to accelerate the convergence of the multi level iterative method by smoothing the residuals of the original iterative sequence the sequence with smoothed residuals is re introduced into the multi level iterative process the new sequence generated by this acceleration procedure converges much faster than both the sequence generated by the original multi level method and the sequence generated by mrs technique the cost of this acceleration scheme is independent of the original operator and in many cases is negligible the emphasis of this paper is on the practical implementation of mrs acceleration techniques in the multi level method the discussions are focused on the two level method because the acceleration scheme is only applied on the finest level of the multi level method numerical experiments using the proposed mrs acceleration scheme to accelerate both the two level and multi level methods are conducted to show the efficiency and the cost effectiveness of this acceleration scheme

complete gabor transformation for signal representation properties of the gabor transformation used for image representation are discussed the properties can be expressed in matrix notation and the complete gabor coefficients can be found by multiplying the inverse of the gabor 1946 matrix and the signal vector the gabor matrix can be decomposed into the product of a sparse constant complex matrix and another sparse matrix that depends only on the window function a fast algorithm is suggested to compute the inverse of the window function matrix enabling discrete signals to be transformed into generalized nonorthogonal gabor representations efficiently a comparison is made between this method and the analytical method the relation between the window function matrix and the biorthogonal functions is demonstrated a numerical computation method for the biorthogonal functions is proposed

a new taxonomy of conjugate gradient methods abstract in this paper a framework is proposed for conjugate gradient and conjugate direction algorithms based on an indefinite quadratic form by the choice of the hessian g of this form and of another arbitrary matrix k no fewer than nineteen distinct cg algorithms may be succinctly defined four of these are believed to be new the choice of certain other vectors leads either to a two term or a three term recurrence formula and it is shown that to every two term formula there corresponds a three term formula although the converse is not generally true the two matrices g and k also determine the stability characteristics of the two term methods

fdem how we make the fdm more flexible than the fem the finite difference element method fdem is a black box solver for the solution of nonlinear systems of elliptic and parabolic pdes an algorithm has been developed to generate on an unstructured fem grid difference formulas of arbitrary consistency order q from the difference of difference formulas of different consistency order an estimate of the discretization error is obtained an error equation permits the explicit following of all errors and gives the prescriptions for the selfadaptation of the method coupled domains with different pdes and different nonmatching grids that slide relative to each other can be treated and a global error estimate is computed thus we get an fdm that is in all aspects more flexible than the fem the whole code is efficiently parallelized on distributed memory parallel computers

vector sequence transformations methodology and applications to linear systems in this paper a methodology for the construction of various vector sequence transformations is formulated leading to a unified presentation of the subject and to new results the connections to the general interpolation problem and to projections are discussed various particular cases are examined in more details applications to the solution of systems of linear equations will end the paper and in particular their relation with lanczos method will be studied some numerical examples will be given

qmr smoothing for lanczos type product methods based on three term rrecurrences for the solution of large sparse non hermitian linear systems lanczos type product methods that are based on the lanczos three term recurrence are derived in a systematic way these methods either square the lanczos process or combine it with a local minimization of the residual for them a quasi minimal residual qmr smoothing is proposed that can also be implemented by short term recurrences the practical performance of these methods and the qmr smoothing is demonstrated in a number of numerical examples

ml n bicgstabt a ml n bicgstab variant with a transpose the 1980 idr method wesseling and sonneveld 1980 12 plays an important role in the history of krylov subspace methods it started the research of transpose free krylov subspace methods the ml n bicgstab method yeung 2012 is one of such methods in this paper we present a new ml n bicgstab variant that involves a transpose in its implementation comparison of this new algorithm with the existing ml n bicgstab algorithms and some other krylov subspace algorithms will be presented

on augmentation block triangular preconditioners for regularized saddle point problems two augmentation block triangular preconditioners were introduced by shen et al 2012 for the regularized saddle point problem however the spectral analysis of the preconditioner based on the augmentation of the 2 2 block was not throughly derived there in this short paper we give a detailed spectral analysis on this preconditioner a numerical example is employed to validate the efficiency of the presented theoretical results

a hybridized iterative algorithm of the bicorstab and gpbicor methods for solving non hermitian linear systems in this study we derive a new iterative algorithm including its preconditioned version which is a hybridized variant of the biconjugate a orthogonal residual stabilized bicorstab method and the generalized product type solvers based on bicor gpbicor method the proposed method which is named gpbicor m similarly to the gpbicg m method proposed by fujino 2002 can be regarded as an extension of the bicorstab2 method introduced by zhao and huang 2013 inspired by fujino s idea for improving the bicgstab2 method in the established gpbicor m method the parameters computed by the bicorstab method are chosen at successive m iteration steps and afterwards the parameters of the gpbicor method are utilized in the subsequent iteration steps therefore the proposed method can inherit the low computational cost of bicorstab and the attractive convergence of gpbicor extensive numerical convergence results on selected real and complex matrices are shown to assess the performances of the proposed gpbicor m method also against other popular non hermitian krylov subspace methods

a variant algorithm of the orthomin m method for solving linear systems abstract we propose a variant of o rthomin m for solving linear systems a x b it is mathematically equivalent to the original o rthomin m method but uses recurrence formulas that are different from those of o rthomin m they contain alternative expressions for the auxiliary vectors and the recurrence coefficients our implementation has the same computational costs as o rthomin m as a result of numerical experiments on nonsingular linear systems we have confirmed the equivalence of our proposed variant of o rthomin m with the original o rthomin m using finite precision arithmetic numerical experiments on singular linear systems show that our proposed algorithm is more accurate and less affected by rounding errors than the original o rthomin m

ml k bicgstab a bicgstab variant based on multiple lanczos starting vectors we present a variant of the popular bicgstab method for solving nonsymmetric linear systems the method which we denote by ml k bicgstab is derived from a variant of the bicg method based on a lanczos process using multiple k 1 starting left lanczos vectors compared with the original bicgstab method our new method produces a residual polynomial which is of lower degree after the same number of steps but which also requires fewer matrix vector products to generate on average requiring only 1 1 k matvecs per step empirically it also seems to be more stable and more quickly convergent the new method can be implemented as a k term recurrence and can be viewed as a bridge connecting the arnoldi based fom gmres methods and the lanczos based bicgstab methods

variants of bicgstab for matrices with complex spectrum recently van der vorst siam j sci statist comput 13 1992 pp 631 644 proposed for solving nonsymmetric linear systems az b a biconjugate gradient bicg based krylov space method called bicgstab that like the biconjugate gradient squared bicgs method of sonneveld does not require matrix vector multiplications with the transposed matrix a t and that has typically a much smoother convergence behavior than bicg and bicgs its nth residual polynomial is the product of the one of bicg i e the nth lanczos polynomial with a polynomial of the same degree with real zeros therefore nonreal eigenvalues of a are not approximated well by the second polynomial factor here the author presents for real nonsymmetric matrices a method bicgstab2 in which the second factor may have complex conjugate zeros moreover versions suitable for complex matrices are given for both methods

idr a new generation of krylov subspace methods the induced dimension reduction idr technique developed by sonneveld and van gijzen is a powerful concept resulting in a variety of transpose free krylov subspace methods based on short term recurrences we present the main di erences between and similarities of idr methods and classical krylov subspace methods our tool of trade is the so called generalized hessenberg decomposition the concept of transfer of techniques from the setting of classical krylov subspace methods to the idr based methods is introduced for simplicity we only sketch some recent results in the fields of eigenvalue computations and of solution of linear systems

an error indicator monitor function for an r adaptive finite element method an r adaptive finite element method based on moving mesh partial differential equations pdes and an error indicator is presented the error indicator is obtained by applying a technique developed by bank and weiser to elliptic equations which result in this case from temporal discretization of the underlying physical pdes on moving meshes the construction of the monitor function based on the error indicator is discussed numerical results obtained with the current method and the commonly used method based on solution gradients are presented and analyzed for several examples c 2001 academic press

exploiting bicgstab ell strategies to induce dimension reduction idr s p sonneveld and m b van gijzen siam j sci comput 31 2008 pp 1035 1062 and bicgstab ell g l g sleijpen and d r fokkema electron trans numer anal 1 1993 pp 11 32 are two of the most efficient short recurrence iterative methods for solving large nonsymmetric linear systems of equations which of the two is best depends on the specific problem class in this paper we describe idrstab a new method that combines the strengths of idr s and bicgstab ell to derive idrstab we extend the results that we reported on in g l g sleijpen p sonneveld and m b van gijzen appl numer math 2009 doi 10 1016 j apnum 2009 07 001 where we considered bi cgstab as an induced dimension reduction idr method we will analyze the relation between hybrid bi cg methods and idr and introduce the new concept of the sonneveld subspace as a common framework through numerical experiments we will show that idrstab can outperform both idr s and bicgstab ell

bicgcr2 a new extension of conjugate residual method for solving non hermitian linear systems abstract in the present paper we introduce a new extension of the conjugate residual cr method for solving non hermitian linear systems with the aim of developing an alternative basic solver to the established biconjugate gradient bicg biconjugate residual bicr and biconjugate a orthogonal residual bicor methods the proposed krylov subspace method referred to as the bicgcr2 method is based on short term vector recurrences and is mathematically equivalent to both bicr and bicor we demonstrate by extensive numerical experiments that the proposed iterative solver has often better convergence performance than bicg bicr and bicor hence it may be exploited for the development of new variants of non optimal krylov subspace methods

a class of product type krylov subspace methods for solving nonsymmetric linear systems abstract in the present paper a class of product type krylov subspace methods for solving nonsymmetric linear systems is discussed a characteristic of this class is the relationship r n h n a r n bcg where r n is the residual vector corresponding to the nth iterate x n and r n bcg is the nth residual generated in bi conjugate gradient method the polynomial hn is chosen to speed up and stabilize convergence while satisfying standard three term recurrence relations these product type methods can be regarded as unifications and generalizations of cgs and bi cgstab

on vector transformation it has been shown that a vector transform is a good tool for digital filtering and image coding this paper addresses some of the issues related to vector transforms first a fundamental difference between vector transforms and conventional transforms is examined second two approaches to constructing vector transforms are discussed finally an application of vector transformation to an efficient implementation of 2 d nonseparable digital filters is proposed

application of the multiplicative regularized gauss newton algorithm for three dimensional microwave imaging we apply the so called multiplicative regularized gauss newton inversion algorithm for solving three dimensional electromagnetic microwave inverse problems this inversion algorithm automatically adjusts the regularization parameter and when combined with the total variation type regularization function it can provide inversion results with excellent edge preserving characteristics in addition in order to deal with an extensive memory requirement for the gauss newton method we employ an implicit jacobian calculation scheme by using this scheme we do not have to explicitly store the jacobian matrix hence we are able to significantly reduce the memory requirement of the gauss newton method albeit at an additional computational overhead furthermore in order to be able to handle a large scale computational problem both the forward and the inversion algorithms are parallelized using the mpi library where we obtain a nearly linear speedup factor we demonstrate efficiency and robustness of this algorithm by inverting synthetic data fresnel experimental data and biomedical experimental data

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

metric tensors for anisotropic mesh generation it has been amply demonstrated that significant improvements in accuracy and efficiency can be gained when a properly chosen anisotropic mesh is used in the numerical solution for a large class of problems which exhibit anisotropic solution features in practice an anisotropic mesh is commonly generated as a quasi uniform mesh in the metric determined by a tensor specifying the shape size orientation of elements thus it is crucial to choose an appropriate metric tensor for anisotropic mesh generation and adaptation in this paper we develop a general formula for the metric tensor for use in any spatial dimension the formulation is based on error estimates for polynomial preserving interpolation on simiplicial elements numerical results in two dimensions are presented to demonstrate the ability of the metric tensor to produce anisotropic meshes with correct mesh concentration and good overall quality the procedure developed in this paper for defining the metric tensor can also be applied to other types of error estimates

bargmann transform zak transform and coherent states it is well known that completeness properties of sets of coherent states associated with lattices in the phase plane can be proved by using the bargmann representation or by using the kq representation which was introduced by j zak in this paper both methods are considered in particular in connection with expansions of generalized functions in what are called gabor series the setting consists of two spaces of generalized functions tempered distributions and elements of the class s which appear in a natural way in the context of the bargmann transform also a thorough mathematical investigation of the zak transform is given this paper contains many comments and complements on existing literature in particular connections with the theory of interpolation of entire functions over the gaussian integers are given

recycling bicgstab with an application to parametric model order reduction krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems based on this technique the recycling bicg algorithm has been developed recently here we now generalize and extend this recycling theory to bicgstab recycling bicg focuses on efficiently solving sequences of dual linear systems while the focus here is on efficiently solving sequences of single linear systems assuming nonsymmetric matrices for recycling bicg and recycling bicgstab as compared with other methods for solving sequences of single linear systems with nonsymmetric matrices e g recycling variants of gmres bicg based recycling algorithms like recycling bicgstab have the advantage that they involve a short term recurrence and hence do not suffer from storage issues and are also cheaper with respect to the orthogonalizations we modify the bicgstab algorithm to use a recycle space which is built from left and right approximate invariant subspaces using our algorithm for a parametr

bicgstab vpastab and an adaptation to mildly nonlinear systems the key equations of bicgstab are summarised to show its connections with pade and vector pade approximation these considerations lead naturally to stabilised vector pade approximation of a vector valued function vpastab and an algorithm for the acceleration of convergence of a linearly generated sequence of vectors a generalisation of this algorithm for the acceleration of convergence of a nonlinearly generated system is proposed here and comparative numerical results are given

a quasi minimal residual variant of the bicorstab method for nonsymmetric linear systems abstract the biconjugate a orthogonal residual stabilized method named as bicorstab was proposed by jing et al 2009 where the numerical experiments therein demonstrate that the bicorstab method converges more smoothly than the bi conjugate gradient stabilized bicgstab method in some circumstances in order to further stabilize the convergence behavior and hopefully to accelerate the convergence speed of the bicorstab algorithm when it has erratic convergence curves a quasi minimal residual variant of the bicorstab algorithm named as qmrcorstab will be developed and investigated for solving nonsymmetric systems of linear equations borrowing the same further smooth effect idea for the qmrcgstab method numerical experiments on typical sets of both sparse and dense matrices will show that the proposed qmrcorstab method shares attractive smoother effect over its basic parent and also outperforms its counterpart

improved fourier and hartley transform algorithms application to cyclic convolution of real data this paper highlights the possible tradeoffs between arithmetic and structural complexity when computing cyclic convolution of real data in the transform domain both fourier and hartley based schemes are first explained in their usual form and then improved either from the structural point of view or in the number of operations involved namely we first present an algorithm for the in place computation of the discrete fourier transform on real data a decimation in time split radix algorithm more compact than the previously published one second we present a new fast hartley transform algorithm with a reduced number of operations a more regular convolution scheme based on fft s is also proposed finally we show that hartley transforms belong to a larger class of algorithms characterized by their generalized convolution property

hybrid bi cg methods with a bi cg formulation closer to the idr approach the induced dimension reduction s idr s method has recently been developed sleijpen et al have reformulated the bi conjugate gradient stabilized bicgstab method to clarify the relationship between bicgstab and idr s the formulation of bi conjugate gradient bi cg part used in the reformulated bicgstab is different from that of the original bi cg method the bi cg coefficients are computed by a formulation that is closer to the idr approach in this paper we will redesign variants of the conjugate gradient squared method cgs method bicgstab and the generalized product type method derived from bi cg gpbicg bicg mr2 by using the bi cg formulation that is closer to the idr approach although our proposed variants are mathematically equivalent to their counterparts the computation of one of the bi cg coefficients differs and the recurrences of the variants are also partly different from those of the original hybrid bi cg methods numerical experiments show that the variants of bicgstab and gpbicg bicg mr2 are more stable and lead to faster convergence typically for linear systems for which the methods converge slowly long stagnation phase and that the variants of cgs attain more accurate approximate solutions

on iterative approaches for electromagnetic rough surface scattering problems iterative techniques developed for solving general systems of linear equations have been applied to systems resulting from electromagnetic rough surface scattering problems previously used iterative procedures that model the multiple scattering of the electromagnetic energy are shown to be mathematically equivalent to the application of stationary iterative procedures to the system of equations resulting from the standard moment method convergence difficulties that are sometimes observed with these approaches are due to the inherent limitations of the stationary techniques the performances of the stationary approaches are compared with that of several conjugate direction based nonstationary iterative procedures through the application to a series of scattering surfaces that yield rapidly changing conditioning of the moment method interaction matrix the stationary algorithms give the quickest convergence when applied to the systems with the best conditioning but the nonstationary techniques prove much more robust in other more ill conditioned situations

a new family of global methods for linear systems with multiple right hand sides the global bi conjugate gradient gl bcg method is an attractive matrix krylov subspace method for solving nonsymmetric linear systems with multiple right hand sides but it often show irregular convergence behavior in many applications in this paper we present a new family of global a biorthogonal methods by using short two term recurrences and formal orthogonal polynomials which contain the global bi conjugate residual gl bcr algorithm and its improved version finally numerical experiments illustrate that the proposed methods are highly competitive and often superior to originals

vpastab j l an iterative method with look ahead for the solution of large sparse linear systems vpastab j l denotes an iterative method designed to give an accurate numerical solution of a large sparse system of linear equations the iteration comprises l steps and possibly jump steps an l step involves stabilisation minimisation over an l dimensional subspace following l levels of vector pade approximation a jump step look ahead stage avoids near breakdowns by jumping past them by j levels simultaneously a numerical implementation of vpastab 2 l is considered in the context of some well known examples

iterative solution of 3d acoustic wave equation with perfectly matched layer boundary condition and multigrid preconditioner abstractwe tested a biconjugate gradient stabilized bicgstab solver using a multigrid based preconditioner for solving the acoustic wave helmholtz equation in the frequency domain the perfectly matched layer pml method was used as the radiation boundary condition rbc the equation was discretized using either a second or fourth order finite difference fd scheme the convergence of an iterative solver depended strongly on the rbc used because the spectrum of the discretized equation also depends on it we used a geometric multigrid approach to construct a preconditioner for our fd frequency domain fdfd forward solver equipped with the pml boundary condition for efficiency this preconditioner was only constructed using a second order fd scheme with negligible attenuation inside the pml domain the preconditioner was used for accelerating the convergence rate of the fdfd forward solver for cases when the discretization grids were oversampled i e when the number of discretization points per

towards monte carlo preconditioning approach and hybrid monte carlo algorithms for matrix computations an enhanced version of a stochastic sparse approximate inverse spai preconditioner for general matrices is presented in this paper this method is used in contrast to the standard deterministic preconditioners computed by the modified sparse approximate inverse preconditioner mspai thus we present a monte carlo preconditioner that relies on the use of markov chain monte carlo mcmc methods to compute a rough approximate matrix inverse first which can further be optimized by an iterative filter process and a parallel refinement to enhance the accuracy of the inverse and the preconditioner respectively the advantage of the proposed approach is that finding the sparse monte carlo matrix inversion has a computational complexity linear of the size of the matrix it is inherently parallel and thus can be obtained very efficiently for large matrices and can be used also as an efficient preconditioner while solving systems of linear algebraic equations the behaviour of the proposed algorithm is studied and its performance measured evaluated and compared with mspai

a quasi minimal residual variant of the bi cgstab algorithm for nonsymmetric systems motivated by a recent method of freund siam j sci comput 14 1993 pp 470 482 who introduced a quasi minimal residual qmr version of the conjugate gradients squared cgs algorithm a qmr variant of the biconjugate gradient stabilized bi cgstab algorithm of van der vorst that is called qmrcgstab is proposed for solving nonsymmetric linear systems the motivation for both qmr variants is to obtain smoother convergence behavior of the underlying method the authors illustrate this by numerical experiments that also show that for problems on which bi cgstab performs better than cgs the same advantage carries over to qmrcgstab

structured fast hartley transform algorithms the flowgraph originally proposed for the computation of the radix 2 fast hartley transform fht is restructured for clarity and ease of implementation with hardware and software by applying the transposition theorem to the newly formed flowgraph which corresponds to a decimation in time algorithm a decimation in frequency algorithm with a similar flowgraph is obtained the number of operations for the two algorithms is the same because of an existing symmetry which is also identical to that of another fht algorithm recently proposed

a moving mesh method based on the geometric conservation law a new adaptive mesh movement strategy is presented which unlike many existing moving mesh methods targets the mesh velocities rather than the mesh coordinates the mesh velocities are determined in a least squares framework by using the geometric conservation law specifying a form for the jacobian determinant of the coordinate transformation defining the mesh and employing a curl condition by relating the jacobian to a monitor function one is able to directly control the mesh concentration the geometric conservation law an identity satisfied by any nonsingular coordinate transformation is an important tool which has been used for many years in the engineering community to develop cell volume preserving finite volume schemes it is used here to transform the algebraic expression specifying the jacobian into an equivalent differential relation which is the key formula for the new mesh movement strategy it is shown that the resulting method bears a close relation with the lagrangian method advantages of the new approach include the ease of controlling the cell volumes and therefore mesh adaption and a theoretical guarantee for existence and nonsingularity of the coordinate transformation it is shown that the method may suffer from the mesh skewness a consequence resulting from its close relation with the lagrangian method numerical results are presented to demonstrate various features of the new method

on the convergence behavior of idr s and related methods an explanation is given of the convergence behavior of idr s methods the convergence mechanism of these algorithms has two components the first consists of damping properties of certain factors in the residual polynomials which becomes less important for large values of s the second component depends on the behavior of lanczos polynomials that occur in the theoretical description this part of the residual polynomials is related to lanczos methods with s left starting vectors as described in a paper by yeung and chan on their ml k bicgstab method in siam j sci comput 21 1999 pp 1263 1290 in this paper the behavior of the second component is compared with the full gmres method siam j sci statist comput 7 1986 pp 856 869 and an expected rate of convergence is given based on a random choice of the s shadow vectors

bicr variants of the hybrid bicg methods for solving linear systems with nonsymmetric matrices we propose bi conjugate residual bicr variants of the hybrid bi conjugate gradient bicg methods referred to as the hybrid bicr variants for solving linear systems with nonsymmetric coefficient matrices the recurrence formulas used to update an approximation and a residual vector are the same as those used in the corresponding hybrid bicg method but the recurrence coefficients are different they are determined so as to compute the coefficients of the residual polynomial of bicr from our experience it appears that the hybrid bicr variants often converge faster than their bicg counterpart numerical experiments show that our proposed hybrid bicr variants are more effective and less affected by rounding errors the factor in the loss of convergence speed is analyzed to clarify the difference of the convergence between our proposed hybrid bicr variants and the hybrid bicg methods

on the sliding window representation in digital signal processing the short time fourier transform of a discrete time signal which is the fourier transform of a windowed version of the signal is interpreted as a sliding window spectrum this sliding window spectrum is a function of two variables a discrete time index which represents the position of the window and a continuous frequency variable it is shown that the signal can be reconstructed from the sampled sliding window spectrum i e from the values at the points of a certain time frequency lattice this sampling lattice is rectangular and the rectangular cells occupy an area of 2 in the time frequency domain it is shown that an elegant way to represent the signal directly in terms of the sample values of the sliding window spectrum is in the form of gabor s signal representation therefore a reciprocal window is introduced and it is shown how the window and the reciprocal window are related gabor s signal representation then expands the signal in terms of properly shifted and modulated versions of the reciprocal window and the expansion coefficients are just the values of the sampled sliding window spectrum

lanczos type variants of the cocr method for complex nonsymmetric linear systems motivated by the celebrated extending applications of the well established complex biconjugate gradient cbicg method to deal with large three dimensional electromagnetic scattering problems by pocock and walker m d pocock s p walker the complex bi conjugate gradient solver applied to large electromagnetic scattering problems computational costs and cost scalings ieee trans antennas propagat 45 1997 140 146 three lanczos type variants of the recent conjugate a orthogonal conjugate residual cocr method of sogabe and zhang t sogabe s l zhang a cocr method for solving complex symmetric linear systems j comput appl math 199 2007 297 303 are explored for the solution of complex nonsymmetric linear systems the first two can be respectively considered as mathematically equivalent but numerically improved popularizing versions of the bicr and crs methods for complex systems presented in sogabe s ph d dissertation and the last one is somewhat new and is a stabilized and more smoothly converging variant of the first two in some circumstances the presented algorithms are with the hope of obtaining smoother and hopefully faster convergence behavior in comparison with the cbicg method as well as its two corresponding variants this motivation is demonstrated by numerical experiments performed on some selective matrices borrowed from the university of florida sparse matrix collection by davis

a generalized product type bicor method and its application in signal deconvolution for solving nonsymmetric linear systems we attempt to establish symmetric structures in nonsymmetric systems and handle them through the methods devised for symmetric cases a biconjugate a orthogonal residual method based on biconjugate a orthonormalization procedure has been proposed and nominated as bicor in y f jing t z huang y zhang l li g h cheng z g ren y duan t sogabe b carpentieri lanczos type variants of the cocr method for complex nonsymmetric linear systems j comput phys 228 2009 6376 6394 as many similar characteristics exist between bicor and bicg the strategies of improved variants of bicg such as cgs and bicgstab can be utilized to enhance the algorithm for bicor making use of the product of residual polynomials of bicor and other polynomials cors and bicorstab have been proposed along the same ideas of cgs and bicgstab respectively in the above mentioned paper in this paper a unified generalized framework of product type bicor which is epitomized by the product of residual polynomials and other polynomials is proposed numerical examples are selected from the blurring signal cases and the effect of the generalized product type bicor method is prominent in signal deconvolution

pixon based image denoising with markov random fields image restoration is an essential preprocessing step for many image analysis applications so far the majority of works have been devoted to image denoising for this issue the most common problem is that some interesting structures in the image will be removed from the concerned image during noise suppression such interesting structures in an image often correspond to the discontinuities in the image in this paper we propose a novel pixon based multiresolution method for image denoising the key idea to our approach is that a pixon map is embedded into a mrf model under a bayesian framework the remarkable advantage of our approach over the existing works in this field is that restoring corrupted images and preserving the shape transitions in the restored results have been orchestrated very well a simulated annealing algorithm is implemented to find the map solution a measure of the performance of various algorithms has been defined and some quantitative comparisons between our approach and two typical filtering techniques have also been done a lot of experiments illustrate that our method is much more effective and powerful in the noise reduction than the wiener and median filtering techniques two typical and widely used techniques c 2001 pattern recognition society published by elsevier science ltd all rights reserved

avoiding breakdown in variants of the bi cgstab algorithm abstract the bi cg method and its variants such as cgs bi cgstab and bi cgstab 2 for solving nonsymmetric linear systems of equations can suffer from breakdown by using the theory of the formal orthogonal polynomials we present a breakdown free bi cgstab algorithm and a breakdown free bi cgstab 2 algorithm only exact breakdowns are cured accurately

stationary nonstationary and hybrid iterative method of moments solution schemes the purpose of this paper is to report on the convergence rates of two iterative matrix solution methods individually and then to combine the two methods into a hybrid scheme to achieve additional convergence rate benefits one iterative matrix solver investigated is the sparse iterative method sim which is a stationary jacobi like solver but uses a sparse and not a banded matrix with matrix elements corresponding to strong interactions rather than position in the matrix in this paper the sim is modified to include an adaptive relaxation scheme to improve its convergence speed and numerical stability another iterative scheme investigated is the nonstationary biconjugate gradient stabilized bicgstab method it is shown that the bicgstab is considerably improved when the method is preconditioned by the sparse matrix used in the sim method finally a hybrid scheme is proposed which combines both sim ar and bicgstab precon and it is shown that the hybrid gives best results on the problems considered examples giving convergence time versus accuracy are presented for two problems a wire grid plate and a wire grid partial helicopter