Spectral analysis of the generalized shift-splitting preconditioned saddle point problem

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• 作者：Zhi-Ru Ren^a ; Yang Cao^b ; ^{caoyangnt@ntu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Qiang Niu^c
• 关键词：65F10 ; 65F50
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：539-550
• 全文大小：558 K

文摘

A shift-splitting preconditioner was recently proposed for saddle point problems, which is based on a generalized shift-splitting of the saddle point matrix. We provide a new analysis to prove that the corresponding shift-splitting iteration method is unconditional convergent. To further show the efficiency of the shift-splitting preconditioner, the eigenvalue distribution of the shift-splitting preconditioned saddle point matrix is investigated. We show that all eigenvalues having nonzero imaginary parts are located in an intersection of two circles and all real eigenvalues are located in a positive interval. Numerical examples are given to confirm our theoretical results.