Optimal Parameter in Hermitian and Skew-Hermitian Splitting Method for Certain Two-by-Two Block Matrices
نویسندگان
چکیده
The optimal parameter of the Hermitian/skew-Hermitian splitting (HSS) iteration method for a real 2-by-2 linear system is obtained. The result is used to determine the optimal parameters for linear systems associated with certain 2-by-2 block matrices, and to estimate the optimal parameters of the HSS iteration method for linear systems with n-by-n real coefficient matrices. Numerical examples are given to illustrate the results.
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 کاملA Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems
In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSSbased iteration methods are proposed for solving weakly nonlinear systems base...
متن کاملA Modified Hss Iteration Method for Solving the Complex Linear Matrix Equation
In this paper, a modified Hermitian and skew-Hermitian splitting (MHSS) iteration method for solving the complex linear matrix equation AXB = C has been presented. As the theoretical analysis shows, the MHSS iteration method will converge under certain conditions. Each iteration in this method requires the solution of four linear matrix equations with real symmetric positive definite coefficien...
متن کاملConvergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices
For the non-Hermitian and positive semidefinite systems of linear equations, we derive sufficient and necessary conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. These result is specifically applied to linear systems of block tridiagonal form to obtain convergence conditions for the corresponding block varia...
متن کاملAn iterative method for solving the continuous sylvester equation by emphasizing on the skew-hermitian parts of the coefficient matrices
We present an iterative method based on the Hermitian and skew-Hermitian splitting for solving the continuous Sylvester equation. By using the Hermitian and skew-Hermitian splitting of the coefficient matrices A and B, we establish a method which is practically inner/outer iterations, by employing a CGNR-like method as inner iteration to approximate each outer iterate, while each outer iteratio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 28 شماره
صفحات -
تاریخ انتشار 2006