On generalized preconditioned Hermitian and skew-Hermitian splitting methods for saddle point problems
نویسنده
چکیده
In this paper, we study the iterative algorithms for saddle point problems(SPP). Bai, Golub and Pan recently studied a class of preconditioned Hermitian and skew-Hermitian splitting methods(PHSS). By further accelerating it with another parameters, using the Hermitian/skew-Hermitian splitting iteration technique we present the generalized preconditioned Hermitian and skew-Hermitian splitting methods with four parameters(4GPHSS). Under some suitable conditions, we give the convergence results. Numerical examples further confirm the correctness of the theory and the effectiveness of the method. Key–Words: Saddle point problems, iterative method, Hermitian and skew-Hermitian splitting method, preconditioned Hermitian and skew-Hermitian splitting method, SOR-like method
منابع مشابه
Convergence Properties of Hermitian and Skew Hermitian Splitting Methods
In this paper we consider the solutions of linear systems of saddle point problems. By using the spectrum of a quadratic matrix polynomial, we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method.
متن کاملGeneralized Accelerated Hermitian and Skew-Hermitian Splitting Methods for Saddle-Point Problems
We generalize the accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems. These methods involve four iteration parameters whose special choices can recover the preconditioned HSS and accelerated HSS iteration methods. Also a new efficient case is introduced and we theoretically prove that this new method converges to the unique solutio...
متن کاملA Generalization of Local Symmetric and Skew-symmetric Splitting Iteration Methods for Generalized Saddle Point Problems
In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Ca...
متن کاملSpectral Properties of the Hermitian and Skew-Hermitian Splitting Preconditioner for Saddle Point Problems
In this paper we derive bounds on the eigenvalues of the preconditioned matrix that arises in the solution of saddle point problems when the Hermitian and skew-Hermitian splitting preconditioner is employed. We also give sufficient conditions for the eigenvalues to be real. A few numerical experiments are used to illustrate the quality of the bounds.
متن کاملSpectral properties of the preconditioned AHSS iteration method for generalized saddle point problems
In this paper, we study the distribution on the eigenvalues of the preconditioned matrices that arise in solving two-by-two block non-Hermitian positive semidefinite linear systems by use of the accelerated Hermitian and skew-Hermitian splitting iteration methods. According to theoretical analysis, we prove that all eigenvalues of the preconditioned matrices are very clustered with any positive...
متن کامل