Sylvester equation

Matrix polynomial

Matrix (chemical analysis)

Algorithm

Physics

Polynomial matrix

Matrix splitting

Mathematical analysis

Spectral radius

Eigenvalues and eigenvectors

Iterative method

Composite material

Materials science

Sylvester matrix

Pure mathematics

State-transition matrix

Applied mathematics

Mathematics

Positive-definite matrix

Symmetric matrix

Quantum mechanics

Polynomial

Hermitian matrix

Applied Mathematics and Computation

In this study, based on the MHSS (Modified Hermitian and skew-Hermitian splitting) method, we will present a generalized MHSS approach for solving large sparse Sylvester equation with non-Hermitian and complex symmetric positive definite/semi-definite matrices. The new method (GMHSS) is a four-parameter iteration procedure where the iterative sequence is unconditionally convergent to the unique solution of the Sylvester equation. Then to improve the GMHSS method, the inexact version of the GMHSS iterative method (IGMHSS) will be described and will be analyzed. Also, by using a new idea, we try to minimize the upper bound of the spectral radius of iteration matrix. Two test problems are given to illustrate the efficiency of the new approach.

A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation