A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations

Zhou, Ru; Wang, Xiang; Tang, Xiaobin

doi:10.1016/j.amc.2015.09.027

Cited by 22 publications

(14 citation statements)

References 44 publications

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“…Based on the idea of matrix splitting and the GHSS method [9], we can split S(A) and S(B) into two skew-Hermitian matrices:…”

Section: Mghss Iteration Methodsmentioning

confidence: 99%

A Modified GHSS Iteration Method for Continuous Sylvester Equation AX+XB=C

Feng¹,

Wu²

2020

Preprint

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This paper is concerned with the modification of a generalization of the Hermitian and skew-Hermitian splitting iteration method for solving large sparse continuous Sylvester equations. The analysis shows that the MGHSS iteration method converges unconditionally to the unique solution of AX+XB=C. An inexact variant of the GHSS iteration method (IMGHSS) has been presented and the analysis of its convergence property in detail has been discussed. Numerical examples are reported to confirm the efficiency of the proposed methods.

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“…Based on the idea of matrix splitting and the GHSS method [9], we can split S(A) and S(B) into two skew-Hermitian matrices:…”

Section: Mghss Iteration Methodsmentioning

confidence: 99%

A Modified GHSS Iteration Method for Continuous Sylvester Equation AX+XB=C

Feng¹,

Wu²

2020

Preprint

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“…For more details about these methods, we refer to [10][11][12]26] and the references therein. This class of methods were also extended to other problems; see [5,7,[27][28][29][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

Jia

Wang

Xiao

2019

Commun. Appl. Math. Comput.

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In this paper, by means of constructing the linear complementarity problems into the corresponding absolute value equation, we raise an iteration method, called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method, for solving the linear complementarity problems whose coefficient matrix in ℝ n×n is large sparse and positive definite. From the convergence analysis, it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions. Numerical examples demonstrate that the presented method precede to other methods in practical implementation.

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“…We refer to [7-14, 16-20, 33, 34, 43] and the references therein. However, using the idea of HSS iteration method to solve matrix equation has not been investigated except for the work in [2,40,42,46,50,51]. In [6], Bai, et al presented a modified HSS iteration method for complex symmetric linear systems of equations.…”

Section: Introductionmentioning

confidence: 99%

A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation $AXB = C$

Zhou¹,

Wang²,

Zhou³

2016

JCM

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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 coefficient matrices, although the original coefficient matrices are complex and non-Hermitian. In addition, the optimal parameter of the new iteration method is proposed. Numerical results show that MHSS iteration method is efficient and robust.

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A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations

Cited by 22 publications

References 44 publications

A Modified GHSS Iteration Method for Continuous Sylvester Equation AX+XB=C

A Modified GHSS Iteration Method for Continuous Sylvester Equation AX+XB=C

The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

A Modified HSS Iteration Method for Solving the Complex Linear Matrix Equation $AXB = C$

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