On modified HSS iteration methods for continuous Sylvester equations

Zhou, Duo; Chen, Guoliang; Cai, Qingyou

doi:10.1016/j.amc.2015.04.020

Cited by 18 publications

(22 citation statements)

References 29 publications

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“…Theoretical analyses and computational results show that the HSS iteration method has the advantages of fast convergence speed, high computation efficiency, and without requirement of symmetry. Future works will also focus on studying the applications of HSS iteration on saddle point problems [9], continuous Sylvester equations [10], and choices of parameters in iteration method [11][12].…”

Section: Resultsmentioning

confidence: 99%

Iteration Methods for Linear Systems with Positive Definite Matrix

Yong¹,

Tuo²,

Shi

2016

TELKOMNIKA

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Section: Resultsmentioning

confidence: 99%

Iteration Methods for Linear Systems with Positive Definite Matrix

Yong¹,

Tuo²,

Shi

2016

TELKOMNIKA

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“…When the matrices A and B are large and sparse, iterative methods are more efficient to solve Eq. (1) such as the Smith , s method [19], the alternating-direction implicit (ADI) method [4,16,21], the HSS and corresponding methods [2,23,27,28], the SSHI method [15], and the KPIM method [20], etc.…”

Section: Introductionmentioning

confidence: 99%

An accelerated Jacobi-gradient based iterative algorithm for solving sylvester matrix equations

Tian

Mao

et al. 2017

Filomat

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In this paper, an accelerated Jacobi-gradient based iterative (AJGI) algorithm for solving Sylvester matrix equations is presented, which is based on the algorithms proposed by Ding and Chen [6], Niu et al. [18] and Xie et al. [25]. Theoretical analysis shows that the new algorithm will converge to the true solution for any initial value under certain assumptions. Finally, three numerical examples are given to verify the eficiency of the accelerated algorithm proposed in this paper.

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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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On modified HSS iteration methods for continuous Sylvester equations

Cited by 18 publications

References 29 publications

Iteration Methods for Linear Systems with Positive Definite Matrix

Iteration Methods for Linear Systems with Positive Definite Matrix

An accelerated Jacobi-gradient based iterative algorithm for solving sylvester matrix equations

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

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