k homology asymptotic representations and unsuspended e theory connes and higson defined a bivariant homology theory e a b for separable c algebras the elements of e a b are taken to be homotopy classes of asymptotic momorphisms from sa k to sb k in symbols e a b sa sb k if a is k nuclear then e theory agrees with kasparov s bivariant k theory we show that in many cases one need not take suspensions to calculate the e theory group e a b for many a we show e a b a b k for all b among the a for which this is true are c0 x pt for x with the homotopy type of a finite connected cw complex this gives a concrete realization of k homology related to the brown douglas fillmore description for example k0 x arises as asymptotic representations k0 x c0 x k other a for which our isomorphic holds include the nonunital dimension drop intervals in this case there is no distinction between homomorphisms and asymptotic morphisms so we have succeeded in classifying all homomorphisms from a dimension drop interval to a stable c algebra this was subsequently used by elliott j reine angew math 443 1993 179 219 in the classification of certain c algebras the dimension drop interval may also be used to describe k x z n in terms of paths of asymptotic representations of c0 x

convergence of generalized aor iterative method for linear systems with strictly diagonally dominant matrices in this paper some improvements on darvishi and hessari on convergence of the generalized aor method for linear systems with diagonally dominant coefficient matrices appl math comput 176 2006 128 133 are presented for bounds of the spectral radius of l w r which is the iterative matrix of the generalized aor gaor method subsequently some new sufficient conditions for convergence of gaor method will be given which improve some results of darvishi and hessari on convergence of the generalized aor method for linear systems with diagonally dominant coefficient matrices appl math comput 176 2006 128 133

on the convergence of the generalized aor method abstract we consider the generalized aor method presented by k r james we give some convergence theorems for various kinds of matrices namely when the coefficient matrix of the linear system is positive definite an h l or m matrix or strictly or irreducibly diagonally dominant

on the theory of wave propagation in anisotropic plates a theoretical framework is developed which describes wave propagation in infinite homogeneous elastic plates of unrestricted anisotropy the approach exploits the propagator matrix which is the exponential of the fundamental elasticity matrix underlying stroh9s formalism of anisotropic elastodynamics the matrices of plate impedance and admittance are introduced and their analytical properties are established which appear fruitful for computing and analysing the plate wave spectra on this basis the dispersion equation can be cast into the form of a real equation involving the monotonic function whose zeros and poles are the wave velocities in a given plate subjected to different boundary conditions traction free or clamped faces it is proved that three fundamental wave branches exist for any orientation of wave propagation in an anisotropic plate with traction free faces and that those branches are missing if one or both faces are clamped the intrinsic symmetry of the wave motion in an arbitrary plate is revealed the general formalism is applied to elaborate the long wavelength low frequency approximation for a thin free plate of unrestricted anisotropy the frequency dispersive wave velocities displacements and tractions at the onset of the fundamental wave branches are derived explicitly the conditions for the extreme velocity values and some other useful universal connections are determined for an arbitrary thin plate and exemplified for specific anisotropy cases

the connes higson construction is an isomorphism let a be a separable c algebra and b a stable c algebra containing a strictly positive element we show that the group ext 1 2 sa b of unitary equivalence classes of extensions of sa by b modulo the extensions which are asymptotically split coincides with the group of homotopy classes of such extensions this is done by proving that the connes higson construction gives rise to an isomorphism between ext 1 2 sa b and the e theory group e a b of homotopy classes of asymptotic homomorphisms from s2a to b

preconditioned gaor methods for solving weighted linear least squares problems in this paper we present the preconditioned generalized accelerated overrelaxation gaor method for solving linear systems based on a class of weighted linear least square problems two kinds of preconditioning are proposed and each one contains three preconditioners we compare the spectral radii of the iteration matrices of the preconditioned and the original methods the comparison results show that the convergence rate of the preconditioned gaor methods is indeed better than the rate of the original method whenever the original method is convergent finally a numerical example is presented in order to confirm these theoretical results

block triangular preconditioners based on symmetric triangular decomposition for generalized saddle point problems abstract in this paper the symmetric triangular decomposition is further studied to construct a class of block triangular preconditioners for generalized saddle point problems such that the preconditioned generalized saddle point matrices are symmetric and positive definite then the preconditioned conjugate gradient iterative method can be used three specific preconditioners are studied in detail eigen properties of the corresponding preconditioned generalized saddle point matrices are studied in particular upper bounds on the condition number of the preconditioned matrices are analyzed finally numerical experiments of a model stokes equation are given to illustrate the efficiency of the new proposed preconditioners

analysis of the dispersion spectrum of fluid loaded anisotropic plates leaky wave branches the supersonic complex velocity versus real frequency dispersion spectrum of the leaky waves in fluid loaded anisotropic plates is discussed utilizing the sextic plate formalism provides approximate solutions for leaky wave velocity in a form that reveals their basic features such as the unique correspondence of the signs of its imaginary part and of the free plate group velocity the relation between the leakage and the rate of frequency dispersion and the principal trends at low high and near cutoff frequencies in arbitrary anisotropic plates a particular thrust of the study is the derivation of closed form asymptotics for the fundamental leaky wave velocity branch es at low frequency and for the continuum of leaky wave branches near the fluid coupled and fluid uncoupled thickness resonances conditions for the asymptotics accuracy are analysed and a comparison between an analytical approximation and exact numerical curves is presented for various cases

symmetric sor method for augmented systems in this paper we develop symmetric successive overrelaxation ssor method to find solution of augmented systems these systems have appeared in many different applications of scientific computing e g the finite element approximation to solve the navier stokes equation and the constrained optimization the convergence of ssor method are studied finally we apply the new method to solve augmented systems the iteration number of this method to receive the solution is very better than sor like method

order reducing conjugate gradients versus block aor for constrained least squares problems abstract we compare the convergence properties of two iterative algorithms for solving equality constrained least squares problems the first algorithm due to barlow nichols and plemmons applies a variation of the conjugate gradient algorithm to a symmetric positive definite system which is smaller than the original problem the second block accelerated overrelaxation is a two parameter generalization of block sor barlow nichols and plemmons have proven that their order reducing conjugate gradient algorithm converges faster than block sor we extend their result to show that the algorithm is also superior to block aor numerical experiments on some structural engineering problems support the analysis

convergences of splitting iterative methods for symmetric indefinite linear systems in this paper we generalize the saddle point problem to general symmetric indefinite systems we also present a kind of convergent splitting iterative methods for the symmetric indefinite systems a special divergent splitting is introduced the sufficient condition is discussed that the eigenvalues of the iteration matrix are real the spectral radius of the iteration matrix is discussed in detail the convergence theories of the splitting iterative methods for the symmetric indefinite systems are obtained finally we present a preconditioner and discuss the eigenvalues of preconditioned matrix

chaotic iterative methods for the linear complementarity problems a class of parallel multisplitting chaotic relaxation methods is established for the large sparse linear complementarity problems and the global and monotone convergence is proved for the h matrix and the l matrix classes respectively moreover comparison theorem is given which describes the influences of the parameters and the multiple splittings upon the monotone convergence rates of the new methods

convergence of gaor method for doubly diagonally dominant matrices abstract in this paper we obtain bounds for the spectral radius of the matrix l r which is the iterative matrix of the generalized accelerated overrelaxation gaor iterative method moreover we present one convergence theorem of the gaor method finally we present two numerical examples

fast solving of weighted pairing least squares systems this paper presents a generalization of the weighted least squares wls named weighted pairing least squares wpls which uses a rectangular weight matrix and is suitable for data alignment problems two fast solving methods suitable for solving full rank systems as well as rank deficient systems are studied computational experiments clearly show that the best method in terms of speed accuracy and numerical stability is based on a special 1 2 3 inverse whose computation reduces to a very simple generalization of the usual cholesky factorization backward substitution method for solving linear systems

a modified sor like method for the augmented systems for the augmented system of linear equations by considering a new splitting of the coefficient matrix a modified sor like msor like method is presented in this paper the convergence of this method is discussed under suitable restrictions on iteration parameters the optimal parameters and the corresponding optimal convergence factor are determined numerical examples are reported to confirm the efficiency of the proposed method

discrete least squares finite element methods abstract a finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators 1 the differential operator defining the spatial boundary value problem and 2 a riesz map on the test space the resulting linear system is overdetermined two different approaches for solving the system are suggested although others are discussed 1 solving the associated normal equation with linear solvers for symmetric positive definite systems e g cholesky factorization and 2 solving the overdetermined system with orthogonalization algorithms e g qr factorization the finite element assembly algorithm for each of these approaches is described in detail the normal equation approach is usually faster for direct solvers and requires less storage the second approach reduces the condition number of the system by a power of two and is less sensitive to round off error the rectangular stiffness matrix of second approach is demonstrated to have condition number o h 1 for a variety of formulations of poisson s equation the stiffness matrix from the normal equation approach is demonstrated to be related to the monolithic stiffness matrices of least squares finite element methods and it is proved that the two are identical in some cases an example with poisson s equation indicates that the solutions of these two different linear systems can be nearly indistinguishable if round off error is not an issue and rapidly converge to each other the orthogonalization approach is suggested to be beneficial for problems which induce poorly conditioned linear systems experiments with poisson s equation in single precision arithmetic as well as the linear acoustics problem near resonance in double precision arithmetic verify this conclusion the methodology described here is an outgrowth of the discontinuous petrov galerkin dpg methodology of demkowicz and gopalakrishnan 2015 the strength of dpg is highlighted throughout however the majority of theory presented is more general extensions to constrained minimization principles are also considered throughout but are not analyzed in experiments

combination of augmented lagrangian technique and st preconditioner for saddle point problems abstract for symmetric indefinite linear systems we introduce a new triangular preconditioner based on symmetric and triangular st decomposition a new 1 1 block is obtained by augmented lagrangian technique the new st preconditioner is introduced by the combination of the new 1 1 block and symmetric and triangular st decomposition then a preconditioned system can be obtained by preconditioning technique which is superior to the original system in terms of condition number we study the spectral properties of preconditioned system such as eigenvalues the estimation of condition number and then give the quasi optimal parameter numerical examples are given to indicate that the new preconditioner has obvious efficiency advantages finally we conclude that the new st preconditioner is a better option to deal with large and sparse problems

analysis of the dispersion spectrum of fluid loaded anisotropic plates flexural type branches and real valued loops abstract the subsonic spectrum of complex velocity versus real frequency in immersed anisotropic plates is considered for the various options of presupposed choice of modes in the loading fluid half spaces two principal implications of the latter prerequisite are investigated the first is related to the family of flexural type branches with origin at v 0 k 0 which evolve from the so called a 0 and a 1 free plate branches in a way that depends on the choice of fluid modes by inspecting the low frequency solutions of the dispersion equations corresponding to the different choices of fluid modes a complete set of the flexural type branches in an anisotropic fluid loaded plate is identified the result generalizes and also rectifies the interpretation commonly adopted for the isotropic case the second issue is concerned with the real valued loops on otherwise complex subsonic branches involving the fluid mode increasing away from the plate this phenomenon has been broadly discussed in numerical and experimental works on isotropic plates the topological origin and shape of the real loops for an arbitrary plate can be readily viewed by way of the graphical layout of the sextic plate formalism to this end three possibilities are considered namely the sound velocity in the fluid c f being i less than the rayleigh velocity ii greater than that but less than the bulk wave threshold in the plate and iii greater than the bulk wave threshold these lead to three basic configurations in case i a closed real loop exists provided than the fluid to solid density ratio is smaller than a certain critical value estimated here in a simple explicit form case ii is typically characterized by the presence of two open real valued arches with common high frequency limits case iii produces an infinite sequence of progressively narrowing real valued arches whose upper arms rise up to c f and then transform into descending curves of solutions associated with the decreasing fluid modes akin to the sezawa continuum a general overview of the locus of looping branches is supplied by analytical estimates and numerical examples

on convergence of the generalized accelerated overrelaxation method in this paper we study the convergence of the generalized accelerated overrelaxation gaor iterative method that is an extension of the classical convergence result of the generalized successive overrelaxation gsor iterative method we proposed some theorems which they obtain better results than similar works by some numerical examples we show the goodness of our results

some new preconditioned generalized aor methods for generalized least squares problems in this paper we present some new preconditioned gaor methods for solving generalized least squares problems and their comparison results comparison results show that the convergence rates of the new preconditioned gaor methods are better than those of the preconditioned gaor methods presented by zhou et al 2009 19 and wang et al 2013 18 whenever these methods are convergent lastly numerical experiments are provided to confirm the theoretical results

numerical methods for generalized least squares problems usually generalized least squares problems are solved by transforming them into regular least squares problems which can then be solved by well known numerical methods however this approach is not very effective in some cases and besides is very expensive for large scale problems in 1979 paige suggested another approach which consists of solving an equivalent equality constrained least squares problem by the orthogonal decomposition the bnp algorithm or the james implicit nullspace iterative methods in this paper we present some new developments of the numerical methods for example 2 cycle sor method and preconditioned conjugate gradient method for generalized least squares problems some numerical comparisons are included as well

the finite product method in the theory of waves and stability this paper presents a method of analysing the dispersion relation and field shape of any type of wave field for which the dispersion relation is transcendental the method involves replacing each transcendental term in the dispersion relation by a finite product polynomial the finite products chosen must be consistent with the low frequency low wavenumber limit but the method is nevertheless accurate up to high frequencies and high wavenumbers full details of the method are presented for a non trivial example that of anti symmetric elastic waves in a layer the method gives a sequence of polynomial approximations to the dispersion relation of extraordinary accuracy over an enormous range of frequencies and wavenumbers it is proved that the method is accurate because certain gamma function expressions which occur as ratios of transcendental terms to finite products largely cancel out nullifying runge s phenomenon the polynomial approximations which are unrelated to taylor series introduce no spurious branches into the dispersion relation and are ideal for numerical computation the method is potentially useful for a very wide range of problems in wave theory and stability theory

on the solution of singular linear systems of algebraic equations by semiiterative methods for a square matrixt n n where i t is possibly singular we investigate the solution of the linear fixed point problemx tx c by applying semiiterative methods sim s to the basic iterationx0 n xk tck 1 c k 1 such problems arise if one splits the coefficient matrix of a linear systemax b of algebraic equations according toa m n m nonsingular which leads tox m 1nx m 1b tx c even ifx tx c is consistent there are cases where the basic iteration fails to converge namely ift possesses eigenvalues 1 with 1 or if 1 is an eigenvalue oft with nonlinear elementary divisors in these cases and also ifx tx c is incompatible we derive necessary and sufficient conditions implying that a sim tends to a vector hat x which can be described in terms of the drazin inverse of i t we further give conditions under which hat x is a solution or a least squares solution of i t x c

generalized aor methods for linear complementarity problem abstract in this paper we firstly establish a class of generalized aor gaor methods for solving a linear complementarity problem lcp m q whose special case reduces to generalized sor gsor method then some sufficient conditions for convergence of the gaor and gsor methods are presented when the system matrix m is an h matrix m matrix and a strictly or irreducible diagonally dominant matrix moreover when m is an l matrix we discuss the monotone convergence of the new methods lastly we report some computational results with the proposed methods

on semi convergence of a class of uzawa methods for singular saddle point problems in this paper a class of uzawa methods are presented for singular saddle point problems these methods contain the recently proposed uzawa aor and uzawa saor methods as special cases the 1 1 block of the corresponding uzawa preconditioner is positive definite both nonsingular and singular preconditioning matrices are considered the semi convergence of these methods is analyzed by using the techniques of singular value decomposition and moore penrose inverse numerical results show that they need less workload per iteration step comparing with the gsor and piu methods in some situations so they are feasible and effective for singular saddle point problems in some situations

a new identity for the surface impedance matrix and its application to the determination of surface wave speeds it is well known in surface wave theory that the secular equation for the surface wave speed can be written as det m 0 in terms of the surface impedance matrix m it is shown in this paper that m satisfies the simple identity m i r t 1 m i r t q 2 i 0 in the usual notation in the stroh formalism this identity provides an efficient method for calculating the wave speed of surface waves in unstressed or pre stressed elastic half spaces the method is explained and illustrated by examples it is also shown that the buckling wrinkling pre stress for a pre stressed elastic half space can be calculated using the same procedure but with pre stress playing the role of

semi convergence analysis of gmssor methods for singular saddle point problems recently some authors darvishi and hessari 2011 zhang et al 2012 discussed the generalized modified symmetric successive over relaxation gmssor method for saddle point problems in this paper we further study the gmssor method for solving singular saddle point problems we prove the semi convergence of the gmssor method without the assumption that the 1 1 block sub matrix a should be symmetric and analyze the spectral property of the corresponding preconditioned matrix numerical experiments are given to illustrate the efficiency of gmssor with appropriate parameters

some results on preconditioned gaor methods in this paper we present preconditioned generalized accelerated overrelaxation methods we compare the spectral radii of the iteration matrices of the preconditioned and original methods the comparison results show that the preconditioned gaor methods converge faster than the gaor method whenever the gaor method is convergent finally we present two numerical examples to confirm our theoretical results

one more pathology of c algebraic tensor products we define a collection of tensor product norms for c algebras and show that a symmetric tensor product functor on the category of separable c algebras need not be associative

modified uzawa methods for saddle point problems abstract in this paper we propose two different modified uzawa methods for solving the saddle point problems and prove the convergence of the proposed methods we solve a lower upper triangular system per iteration in the proposed methods instead of only solving a lower one numerical experiments show that our proposed methods with four parameters perform much faster than previous uzawa methods with three parameters

the complex phase gradient method applied to leaky lamb waves the classical phase gradient method applied to the characterization of the angular resonances of an immersed elastic plate i e the angular poles of its reflection coefficient r was proved to be efficient when their real parts are close to the real zeros of r and their imaginary parts are not too large compared to their real parts this method consists of plotting the partial reflection coefficient phase derivative with respect to the sine of the incidence angle considered as real versus incidence angle in the vicinity of a resonance this curve exhibits a breit wigner shape whose minimum is located at the pole real part and whose amplitude is the inverse of its imaginary part however when the imaginary part is large this method is not sufficiently accurate compared to the exact calculation of the complex angular root an improvement of this method consists of plotting in 3d in the complex angle plane and at a given frequency the angular phase derivative with respect to the real part of the sine of the incidence angle considered as complex when the angular pole is reached the 3d curve shows a clear cut transition whose position is easily obtained

convergence of a generalized mssor method for augmented systems recently wu et al s l wu t z huang x l zhao a modified ssor iterative method for augmented systems j comput appl math 228 1 2009 424 433 introduced a modified ssor mssor method for augmented systems in this paper we establish a generalized mssor gmssor method for solving the large sparse augmented systems of linear equations which is the extension of the mssor method furthermore the convergence of the gmssor method for augmented systems is analyzed and numerical experiments are carried out which show that the gmssor method with appropriate parameters has a faster convergence rate than the mssor method with optimal parameters

a modified ssor iterative method for augmented systems golub wu and yuan g h golub x wu j y yuan sor like methods for augmented systems bit 41 2001 71 85 have presented the sor like algorithm to solve augmented systems in this paper we present the modified symmetric successive overrelaxation mssor method for solving augmented systems which is based on darvishi and hessari s work above we derive its convergence under suitable restrictions on the iteration parameter determine its optimal iteration parameter and the corresponding optimal convergence factor under certain conditions finally we apply the mssor method to solve augmented systems

variants of the uzawa method for saddle point problem in this paper we first propose three variants of the uzawa method for solving the saddle point problem and then we provide convergence results for the three proposed methods numerical experiments show that our proposed methods with three parameters perform about twice as fast as the gsor generalized sor method with two parameters since the proposed methods have less workload per iteration than the gsor

modified aor methods for linear complementarity problem in order to solve a linear complementarity problem lcp m q when m is a 2 cyclic matrix a class of modified aor maor methods based on maor methods for solving linear system whose special case reduces modified sor msor method is proposed some sufficient conditions for convergence of the maor and msor methods are given when the system matrix m is an h matrix m matrix and a strictly or irreducible diagonally dominant matrix when m is an l matrix their monotone convergence are discussed

a note on two block sor methods for sparse least squares problems abstract we compare two recently proposed block sor methods for the solution of large least squares problems with the conjugate gradient algorithm for solving the specially preconditioned normal equations by proving that all three methods are based on the same krylov sequence we show that the conjugate gradient algorithm is generally preferable to the two sor approaches

evaluation of st preconditioners for saddle point problems the general block st decomposition of the saddle point problem is used as a preconditioner to transform the saddle point problem into an equivalent symmetric and positive definite system such a decomposition is called a block st preconditioner two general block st preconditioners are proposed for saddle point problems with symmetric and positive definite 1 1 block some estimations of the condition number of the preconditioned system are given the same study is done for singular 1 1 block

the matrix analogue of the scalar aor iterative method the accelerated overrelaxation aor and the generalized aor gaor iterative methods for the solution of linear systems of algebraic equations a x b a c n i n det a 0 b c n have been around for about four decades and a plethora of variations of them have been proposed in this work a novel algorithm is introduced the matrix analogue of the aor maaor iterative method which is analysed and studied the maaor method generalizes both the aor and the gaor sufficient convergence conditions for the gaor method are determined when the coefficient matrix a of the linear system to be solved is a hermitian matrix with positive diagonal elements similarly sufficient convergence conditions for the maaor method are determined when a is a nonsingular h matrix the new convergence conditions are the most general ones so far numerical examples are presented in support of the theory developed

two new preconditioned gaor methods for weighted linear least squares problems abstract in this paper the preconditioned generalized accelerated overrelaxation gaor methods for solving weighted linear least squares problems are considered two new preconditioners are proposed and the convergence rates of the new preconditioned gaor methods are studied comparison results show that the convergence rates of the new preconditioned gaor methods are better than those of the preconditioned gaor methods in the previous literatures whenever these methods are convergent a numerical example is given to confirm our theoretical results

convergence of relaxation iterative methods for saddle point problem in this paper we first provide convergence results of three relaxation iterative methods for solving saddle point problem next we propose how to find near optimal parameters for which preconditioned krylov subspace method performs nearly best when the relaxation iterative methods are applied to the preconditioners of krylov subspace method lastly we provide efficient implementation for the relaxation iterative methods and efficient computation for the preconditioner solvers numerical experiments show that the miaor method and the bicgstab with maor preconditioner using near optimal parameters perform more than twice faster than the gsor method

preconditioned conjugate gradient method for generalized least squares problems abstract a variant of the preconditioned conjugate gradient method to solve generalized least squares problems is presented if the problem is min ax b t w 1 ax b with a r m n and w r m m symmetric and positive definite the method needs only a preconditioner a 1 r n n but not the inverse of matrix w or of any of its submatrices freund s comparison result for regular least squares problems is extended to generalized least squares problems an error bound is also given

a class of new extended shift splitting preconditioners for saddle point problems abstract in this paper a class of new extended shift splitting ness preconditioners containing t 0 are proposed for saddle point problems which contain the existing shift splitting based preconditioners as special cases the convergence properties of the ness iteration and the spectral distribution of the ness preconditioned matrix are investigated we give an estimated bound for the real eigenvalues of the ness preconditioned matrix whose left end is positive and show that the non real eigenvalues of the ness preconditioned matrix are located in an intersection of two rings particularly these non real eigenvalues are located in an intersection of two rings and one circle if t 1 2 moreover we show that under appropriate conditions our proposed eigenvalue bounds are tighter than the corresponding bounds given in ren et al 2017 using fourier analysis we derive an optimized parameter t independent of the viscosity for the continuous version of the ness preconditioned gmres method for the 2d stokes equation moreover we find that the ness preconditioned gmres method with a constant multiple of the optimized parameter t is effective and robust to solve 2d stokes problems in practice numerical experiments are used to verify our theoretical results

doubly diagonally dominant matrices we consider the class of doubly diagonally dominant matrices a ajj e c la 1 l jjl ck i laiklck jlajkl i j and its subclasses we give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an h matrix as in the case of diagonal dominance we show that the schur complements of doubly diagonally dominant matrices inherit this property moreover we describe when a schur complement of a strictly doubly diagonally dominant matrix is strictly diagonally dominant 0 elsevier science inc 1997 1 preliminaries

a note on preconditioning for the 3 3 block saddle point problem abstract in this paper we mainly propose some new preconditioners for a special class of 3 3 block saddle point problems which can arise from the time dependent maxwell equations and some other practical problems firstly the solvability of this kind of problem is investigated under suitable assumptions then we analyze the corresponding eigenvalues of the new preconditioned matrices presented in this work furthermore we show that proposed preconditioned matrices only have at most three distinct eigenvalues finally two numerical examples are also carried to verify the effectiveness of proposed preconditioners

approximation of the flexural velocity branch in plates the fitting of the flexural velocity branch by means of the pade approximation is examined its use for free isotropic plates is elaborated and compared to other approaches the flexural velocity expansion into power series which underlies the pade implementation is detailed the generalization for fluid loaded plates and inhomogeneous plates is outlined and the impact of anisotropy is discussed in some detail

on convergence of the generalized aor method for linear systems with diagonally dominant coefficient matrices abstract in this paper we obtain bounds for the spectral radius of the matrix l r which is the iterative matrix of generalized accelerated overrelaxation gaor iterative method we consider a linear system hy f where h is an n n diagonally dominant real matrix f is an n real vector of known values and y is an n real vector of unknown variables sufficient conditions for the convergence of gaor method will be presented

a modified symmetric successive overrelaxation method for augmented systems in this paper we establish a modified symmetric successive overrelaxation mssor method to solve augmented systems of linear equations which uses two relaxation parameters this method is an extension of the symmetric sor ssor iterative method the convergence of the mssor method for augmented systems is studied numerical examples show that the new method is an efficient method

an accelerated symmetric sor like method for augmented systems abstract recently njeru and guo presented an accelerated sor like asor method for solving the large and sparse augmented systems in this paper we establish an accelerated symmetric sor like assor method which is an extension of the asor method furthermore the convergence properties of the assor method for augmented systems are studied under suitable restrictions and the functional equation between the iteration parameters and the eigenvalues of the relevant iteration matrix is established in detail finally numerical examples show that the assor is an efficient iteration method

on convergence of two stage splitting methods for linear complementarity problems in this paper we study the splitting method and two stage splitting method for the linear complementarity problems convergence results for these two methods are presented when the system matrix is an h matrix and the splittings used are h splitting numerical experiments show that the two stage splitting method has the same or even better numerical performance than the splitting method in some aspects under certain conditions

convergence of the generalized aor method a generalized aor gaor method is proposed here to solve the linear system with some special structure the convergence of the gaor method is studied the convergence result obtained here is an extension of the classical convergence result of the regular aor method with weaker condition in comparing with the generalized sor gsor method we show that the gaor method is better than the gsor method under certain conditions in some cases the gaor method is convergent even if the gsor method does not converge finally the gaor method is applied to solve the generalized least squares ls problems three numerical algorithms for the generalized ls problems are given

variants of the uzawa method for three order block saddle point problem abstract in this paper we first propose three kinds of variants of the uzawa method for solving three order block saddle point problem and study the convergence conditions of the proposed methods second we obtain the approximate optimal relaxation factors of the three proposed uzawa type methods by using variable control method finally the experimental results show that our proposed uzawa type methods for solving three order block saddle point problem have less workload per iteration step than the corresponding uzawa type methods for solving standard saddle point problem which explains that our proposed methods are feasible and efficient