SPECTRAL ANALYSIS OF THE MGSS PRECONDITIONER FOR SINGULAR SADDLE POINT PROBLEMS

被引：1

作者：

Rahimian, Maryam ^{[1
]}

Salkuyeh, Davod Khojasteh ^{[1
]}

机构：

[1] Univ Guilan, Fac Math Sci, Rasht, Iran

来源：

JOURNAL OF APPLIED MATHEMATICS & INFORMATICS | 2020年 / 38卷 / 1-2期

关键词：

Saddle point problem; Singular; preconditioner; eigenvalue; symmetric positive definite; bound; SHIFT-SPLITTING PRECONDITIONER;

D O I：

10.14317/jami.2020.175

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.

引用

页码：175 / 187

页数：13

共 16 条

[11] Saad Yousef, 2003, ITERATIVE METHODS SP, DOI DOI 10.1137/1.9780898718003
[12] Salkuyeh D.K., 2015, 46 ANN IR MATH C YAZ
[13] A modification of the generalized shift-splitting method for singular saddle point problems
Salkuyeh, Davod Khojasteh
Rahimian, Maryam
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (12) : 2940 - 2949
[14] On the generalized shift-splitting preconditioner for saddle point problems
Salkuyeh, Davod Khojasteh
Masoudi, Mohsen
Hezari, Davod
[J]. APPLIED MATHEMATICS LETTERS, 2015, 48 : 55 - 61
[15] Generalized shift-splitting preconditioners for nonsingular and singular generalized saddle point problems
Shen, Qin-Qin
Shi, Quan
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (03) : 632 - 641
[16] On semi-convergence of parameterized Uzawa methods for singular saddle point problems
Zheng, Bing
Bai, Zhong-Zhi
Yang, Xi
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (5-7) : 808 - 817

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