bounded error identification of hammerstein systems through sparse polynomial optimization in this paper we present a procedure for the evaluation of bounds on the parameters of hammerstein systems from output measurements affected by bounded errors the identification problem is formulated in terms of polynomial optimization and relaxation techniques based on linear matrix inequalities are proposed to evaluate parameter bounds by means of convex optimization the structured sparsity of the formulated identification problem is exploited to reduce the computational complexity of the convex relaxed problem analysis of convergence properties and computational complexity is reported

a generalized shift splitting preconditioner for complex symmetric linear systems abstract in this paper the generalized shift splitting gss preconditioner is implemented for solving a class of generalized saddle point problems which stem from the solution of complex symmetric linear systems the gss preconditioner is induced by the generalized shift splitting iterative method theoretical analysis shows that the generalized shift splitting iterative method is unconditionally convergent some numerical experiments are provided to show the effectiveness of the proposed preconditioner

uzawa type algorithms for nonsymmetric saddle point problems in this paper we consider iterative algorithms of uzawa type for solving linear nonsymmetric saddle point problems specifically we consider systems written as usual in block form where the upper left block is an invertible linear operator with positive definite symmetric part such saddle point problems arise for example in certain finite element and finite difference discretizations of navier stokes equations oseen equations and mixed finite element discretization of second order convection diffusion problems we consider two algorithms each of which utilizes a preconditioner for the operator in the upper left block convergence results for the algorithms are established in appropriate norms the convergence of one of the algorithms is shown assuming only that the preconditioner is spectrally equivalent to the inverse of the symmetric part of the operator the other algorithm is shown to converge provided that the preconditioner is a sufficiently accurate approximation of the inverse of the upper left block applications to the solution of steady state navier stokes equations are discussed and finally the results of numerical experiments involving the algorithms are presented

on semi convergence of the generalized shift splitting iteration method for singular nonsymmetric saddle point problems recently a class of generalized shift splitting iteration methods were proposed for solving nonsingular nonsymmetric saddle point problems cao et al 2015 in this paper the generalized shift splitting iteration method is extended to solve singular nonsymmetric saddle point problems semi convergence of the generalized shift splitting iteration method is carefully analyzed which shows that the iterative sequence generated by the generalized shift splitting iteration method converges to a solution of the singular saddle point problem unconditionally numerical results verify the robustness and efficiency of the generalized shift splitting iteration method

on semi convergence of parameterized uzawa methods for singular saddle point problems abstract bai et al recently proposed an efficient parameterized uzawa method for solving the nonsingular saddle point problems z z bai b n parlett z q wang on generalized successive overrelaxation methods for augmented linear systems numer math 102 2005 1 38 in this paper we further prove the semi convergence of this method when it is applied to solve the singular saddle point problems under suitable restrictions on the involved iteration parameters the optimal iteration parameters and the corresponding optimal semi convergence factor for the parameterized uzawa method are determined in addition numerical experiments are used to show the feasibility and effectiveness of the parameterized uzawa method for solving singular saddle point problems

on preconditioned generalized shift splitting iteration methods for saddle point problems abstract we study a preconditioned generalized shift splitting iteration method for solving saddle point problems the unconditional convergence theory of the preconditioned generalized shift splitting iteration method is established when the splitting matrix is used as a preconditioner we analyze eigenvalue distribution of the preconditioned saddle point matrix it is proved that complex eigenvalues having nonzero imaginary parts of the preconditioned matrix are located in an intersection of two circles and the real parts of all eigenvalues of the preconditioned matrix are located in a positive interval numerical experiments are used to verify our theoretical results and illustrate effectiveness of the proposed iteration method and the corresponding splitting preconditioner

new local generalized shift splitting preconditioners for saddle point problems based on a local generalized shift splitting of the saddle point matrix with symmetric positive definite 1 1 block and symmetric positive semidefinite 2 2 block a new local generalized shift splitting preconditioner with two shift parameters for solving saddle point problems is proposed the preconditioner is extracted from a new local generalized shift splitting iteration and can lead to the unconditional convergence of the iteration in addition we consider solving the saddle point systems by preconditioned krylov subspace methods and discuss some properties of the preconditioned saddle point matrix with a deteriorated preconditioner such as eigenvalues eigenvectors and degree of the minimal polynomial numerical experiments arising from a finite element discretization model of the stokes problem are given to validate the effectiveness of the proposed preconditioner

a unified approach for uzawa algorithms we present a unified approach in analyzing uzawa iterative algorithms for saddle point problems we study the classical uzawa method the augmented lagrangian method and two versions of inexact uzawa algorithms the target application is the stokes system but other saddle point systems e g arising from mortar methods or lagrange multipliers methods can benefit from our study we prove convergence of uzawa algorithms and find optimal rates of convergence in an abstract setting on finite or infinite dimensional hilbert spaces the results can be used to design multilevel or adaptive algorithms for solving saddle point problems the discrete spaces do not have to satisfy the lbb stability condition

on parameterized inexact uzawa methods for generalized saddle point problems abstract for the large sparse saddle point problems bai et al recently studied a class of parameterized inexact uzawa piu methods z z bai b n parlett z q wang on generalized successive overrelaxation methods for augmented linear systems numer math 102 2005 1 38 for a special case that the 1 1 block is solved exactly they determined the convergence domain and computed the optimal iteration parameters and the corresponding optimal convergence factor for the induced method in this paper we develop these methods to the large sparse generalized saddle point problems for the obtained parameterized inexact uzawa method we prove its convergence under suitable restrictions on the iteration parameters in particular we determine its quasi optimal iteration parameters and the corresponding quasi optimal convergence factor for the saddle point problems furthermore this piu method is generalized to obtain a framework of accelerated variants of the parameterized inexact uzawa methods for solving both symmetric and nonsymmetric generalized saddle point problems by using the techniques of vector extrapolation matrix relaxation and inexact iteration

on generalized successive overrelaxation methods for augmented linear systems for the augmented system of linear equations golub wu and yuan recently studied an sor like method bit 41 2001 71 85 by further accelerating it with another parameter in this paper we present a generalized sor gsor method for the augmented linear system we prove its convergence under suitable restrictions on the iteration parameters and determine its optimal iteration parameters and the corresponding optimal convergence factor theoretical analyses show that the gsor method has faster asymptotic convergence rate than the sor like method also numerical results show that the gsor method is more effective than the sor like method when they are applied to solve the augmented linear system this gsor method is further generalized to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation matrix relaxation and inexact iteration besides we also demonstrate a complete version about the convergence theory of the sor like method

on the semi convergence of regularized hss iteration methods for singular saddle point problems abstract recently bai and benzi proposed a class of regularized hermitian and skew hermitian splitting rhss iteration methods for solving the nonsingular saddle point problem in this paper we apply this method to solve the singular saddle point problem in the process of the semi convergence analysis we get that the rhss method and the hss method are unconditionally semi convergent which has improved the previous results then some spectral properties of the corresponding preconditioned matrices and a class of improved preconditioned matrices are analyzed finally some numerical experiments on linear systems arising from the discretization of the stokes equation are presented to illustrate the feasibility and effectiveness of this method and the corresponding preconditioners

residual reduction algorithms for nonsymmetric saddle point problems in this paper we introduce and analyze uzawa algorithms for non symmetric saddle point systems convergence for the algorithms is established based on new spectral results about schur complements a new uzawa type algorithm with optimal relaxation parameters at each new iteration is introduced and analyzed in a general framework numerical results supporting the efficiency of the algorithms are presented for finite element discretization of steady state navier stokes equations

on semi convergence of the uzawa hss method for singular saddle point problems based on the hermitian and skew hermitian splitting hss iteration scheme an efficient uzawa hss iteration method has been proposed to solve the nonsingular saddle point problems in this paper we discuss the feasibility of the uzawa hss method used for solving singular saddle point problems the semi convergence properties of the uzawa hss iteration method are carefully analyzed which show that the iterative sequence generated by the uzawa hss method converges to a solution of the singular saddle point problem if the iteration parameters satisfy suitable restrictions numerical results verify the robustness and efficiency of the uzawa hss method

on the nonlinear inexact uzawa algorithm for saddle point problems this paper discusses convergence behavior of the nonlinear inexact uzawa algorithm for solving saddle point problems presented in a recent paper of bramble pasciak and vassilev siam j numer anal 34 1997 pp 1072 1092 it is shown that this algorithm converges under a condition weaker than that stated in their paper

shift splitting preconditioners for saddle point problems in this paper we first present a shift splitting preconditioner for saddle point problems the preconditioner is based on a shift splitting of the saddle point matrix resulting in an unconditional convergent fixed point iteration based on the idea of the splitting we further propose a local shift splitting preconditioner some properties of the local shift splitting preconditioned matrix are studied these preconditioners extend those studied by bai yin and su for solving non hermitian positive definite linear systems bai et al 2006 finally numerical experiments of a model stokes problem are presented to show the effectiveness of the proposed preconditioners

a class of efficient parameterized shift splitting preconditioners for block two by two linear systems abstract based on the effective constructing an equivalent block two by two linear systems we establish a class of efficient parameterized shift splitting eps preconditioners for solving block two by two linear systems theoretical analysis shows that the eps iteration method is unconditionally convergent and then we study the spectral properties of the corresponding preconditioned matrix by removing one of the shift term of the eps preconditioners two classes of local eps preconditioners are presented and the eigenvalues distribution of the preconditioned matrices are also studied numerical experiments are provided to demonstrate the feasibility and effectiveness of the proposed preconditioners

the generalized modified shift splitting preconditioners for nonsymmetric saddle point problems for a nonsymmetric saddle point problem the modified shift splitting mss preconditioner has been proposed by zhou et al by replacing the parameter in 2 2 block in the mss preconditioner by another parameter a generalized mss gmss preconditioner is established in this paper which results in a fixed point iteration called the gmss iteration method we provide the convergent and semi convergent analysis of the gmss iteration method which show that this method is convergence and semi convergence if the related parameters satisfy suitable restrictions meanwhile the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analyzed in detail finally numerical examples show that the gmss method is more feasibility and robustness than the mss uzawa hss and pu sts methods as a solver and the gmss preconditioner outperforms the gsor uzawa hss mss and lmss preconditioners for the gmres method for solving both the nonsingular and the singular saddle point problems with nonsymmetric positive definite and symmetric dominant 1 1 parts

convergence analysis of modified pgss methods for singular saddle point problems abstract recently variants of shift splitting iteration method have been proposed for solving singular saddle point problems however these methods can only be proved to converge to one of the solutions of the consistent singular linear system not knowing any further information about this solution in this work we consider a modified preconditioned generalized shift splitting mpgss iteration method for solving both consistent and inconsistent singular saddle point problems this method is proved to converge to the best least squares solution moreover based on the iteration form a preconditioner is obtained to accelerate krylov subspace methods theoretical analysis shows that the preconditioned gmres method also converges to the best least squares solution of the consistent singular saddle point problem in addition numerical results are presented to show the effectiveness and robustness of the proposed iteration method and preconditioner

a modification of the generalized shift splitting method for singular saddle point problems abstract a modification of the generalized shift splitting gss method is presented for solving singular saddle point problems in this kind of modification the diagonal shift matrix is replaced by a block diagonal matrix which is symmetric positive definite semi convergence of the proposed method is investigated the induced preconditioner is applied to the saddle point problem and the preconditioned system is solved by the restarted generalized minimal residual method eigenvalue distribution of the preconditioned matrix is also discussed finally some numerical experiments are given to show the effectiveness and robustness of the new preconditioner numerical results show that the modified gss method is superior to the classical gss method

reduce shadow size in aspect ratio invariant visual secret sharing schemes using a square block wise operation an aspect ratio invariant visual secret sharing arivss scheme is a perfectly secure method for sharing secret images due to the nature of the vss encryption each secret pixel is expanded to m sub pixels in each of the generated shares the advantage of arivss is that the aspect ratio of the recovered secret image is fixed and thus there is no loss of information when the shape of the secret image is our information for example a secret image of a circle is compromised to an ellipse if m does not have a square value two arivss schemes based on processing one and four pixel blocks respectively were previously proposed in this paper we have generalized the square block wise approach to further reduce pixel expansion