BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems

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• 作者：Xian-Ming Gu^a ; ^b ; ^{guxianming@live.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{x.m.gu@rug.nl" class="auth_mail" title="E-mail the corresponding author} ; Ting-Zhu Huang^a ; ^{tingzhuhuang@126.com" class="auth_mail" title="E-mail the corresponding author} ; Bruno Carpentieri^c ; ^{bcarpentieri@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65F12 ; 65L05 ; 65N22
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：115-128
• 全文大小：1454 K

文摘

In the present paper, we introduce a new extension of the conjugate residual (CR) method for solving non-Hermitian linear systems with the aim of developing an alternative basic solver to the established biconjugate gradient (BiCG), biconjugate residual (BiCR) and biconjugate class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716301595&_mathId=si15.gif&_user=111111111&_pii=S0377042716301595&_rdoc=1&_issn=03770427&md5=69a2543c8d11ee85a5df7e0a5643cd60" title="Click to view the MathML source">Aclass="mathContainer hidden">class="mathCode">$A$-orthogonal residual (BiCOR) methods. The proposed Krylov subspace method, referred to as the BiCGCR2 method, is based on short-term vector recurrences and is mathematically equivalent to both BiCR and BiCOR. We demonstrate by extensive numerical experiments that the proposed iterative solver has often better convergence performance than BiCG, BiCR and BiCOR. Hence, it may be exploited for the development of new variants of non-optimal Krylov subspace methods.