Abstract
Based on the MHSS (Modified Hermitian and skew-Hermitian splitting) and preconditioned MHSS methods, we will present a generalized preconditioned MHSS method for solving a class of complex symmetric linear systems. The new method (GPMHSS) is essentially a two-parameter iteration method where the iterative sequence is unconditionally convergent to the unique solution of the linear system. A parameter region of the convergence for our method is provided. An efficient preconditioner is presented for the actual implementation of the new method. Some numerical results are given to show its effectiveness.
Highlights
In the paper, we consider the iterative solution of the linear system of the formAx = b, where A ∈ Cn×n is a complex symmetric matrix of the formA = W + iT (1.1) (1.2)M
We present several numerical experiments to show the efficiency of the GPMHSS iteration method, when it is used either as a solver or as a preconditioner for solving the linear system (1.1)–(1.2)
We use x(0) = 0 for the initial guess and the stopping criteria for outer iterations is b − Ax(k) 2/ b 2 < 10−6
Summary
We consider the iterative solution of the linear system of the form. M. IT respectively, A is non-Hermitian positive definite matrix Based on this Hermitian and skew-Hermitian splitting of the matrix A ∈ Cn×n, Bai et al [8] proposed iterative method HSS, to compute an approximate solution for the complex symmetric linear system (1.1)–(1.2). In [4] a modification of the HSS iteration scheme was presented that has the advantage that the solution of linear system with coefficient matrix αI + iT is avoided and only two linear subsystems with coefficient matrices αI + W and αI + T need to be solved at each step.
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