On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

doi:10.1007/s42967-020-00072-8

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (1): 177-187.doi: 10.1007/s42967-020-00072-8

• ORIGINAL PAPER • 上一篇

On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

Ju, Li Zhang

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China

收稿日期:2019-12-26 修回日期:2020-04-12 发布日期:2021-03-15
通讯作者: Ju-Li Zhang, xzhzhangjuli@163.com E-mail:xzhzhangjuli@163.com

On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

Ju, Li Zhang

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China

Received:2019-12-26 Revised:2020-04-12 Published:2021-03-15
Contact: Ju-Li Zhang, xzhzhangjuli@163.com E-mail:xzhzhangjuli@163.com

摘要/Abstract

摘要： In this paper, for the regularized Hermitian and skew-Hermitian splitting (RHSS) preconditioner introduced by Bai and Benzi (BIT Numer Math 57: 287–311, 2017) for the solution of saddle-point linear systems, we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters. We accurately describe the numbers of eigenvalues clustered at (0, 0) and (2, 0), if the iteration parameter is close to 0. An estimate about the condition number of the corresponding eigenvector matrix, which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method, is also studied in this work.

关键词: Saddle-point linear systems, RHSS preconditioner, Preconditioning properties, Matrix similar transformation, Condition number of eigenvector matrix

Abstract: In this paper, for the regularized Hermitian and skew-Hermitian splitting (RHSS) preconditioner introduced by Bai and Benzi (BIT Numer Math 57: 287–311, 2017) for the solution of saddle-point linear systems, we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters. We accurately describe the numbers of eigenvalues clustered at (0, 0) and (2, 0), if the iteration parameter is close to 0. An estimate about the condition number of the corresponding eigenvector matrix, which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method, is also studied in this work.

Key words: Saddle-point linear systems, RHSS preconditioner, Preconditioning properties, Matrix similar transformation, Condition number of eigenvector matrix

中图分类号:

65F10
75N50

Ju, Li Zhang. On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems[J]. Communications on Applied Mathematics and Computation, 2021, 3(1): 177-187.

参考文献

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On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

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