Discrete mathematical models in the analysis of splitting iterative methods for linear systems

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• 作者：Bego&#xf1 ; a Cant&#xf3 ; Carmen Coll ; Elena S&#xe1 ; nchez
• 关键词：Iterative methods ; Descriptor systems ; Stability property ; Convergence ; Discrete models
• 刊名：Computers and Mathematics with Applications
• 出版年：2008
• 期刊代码：37_08981221
• 类别：cp
• 出版时间：August 2008
• 卷：56
• 期：3
• 页码：727-732
• 文件大小：230 K

摘要

Splitting methods are used to solve most of the linear systems, f="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4SBYYH3-1&_mathId=mml1&_user=1067359&_cdi=5620&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=127ff2b10bfdb507844492c26726ce96" title="Click to view the MathML source" alt="Click to view the MathML source">Ax=b, when the conventional method of Gauss is not efficient. These methods use the factorization of the square matrix f="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4SBYYH3-1&_mathId=mml2&_user=1067359&_cdi=5620&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=3fca04eead4e792ac9446abce2db4afc" title="Click to view the MathML source" alt="Click to view the MathML source">A into two matrices f="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4SBYYH3-1&_mathId=mml3&_user=1067359&_cdi=5620&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=88bb90079959388f3ec8573b17663a49" title="Click to view the MathML source" alt="Click to view the MathML source">M and f="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4SBYYH3-1&_mathId=mml4&_user=1067359&_cdi=5620&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=341966b09125d1a863c3e61e6a855271" title="Click to view the MathML source" alt="Click to view the MathML source">N as f="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4SBYYH3-1&_mathId=mml5&_user=1067359&_cdi=5620&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=fb6754f05b7f0fa3b7e950f7afd595a8" title="Click to view the MathML source" alt="Click to view the MathML source">A=M−N where f="/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4SBYYH3-1&_mathId=mml6&_user=1067359&_cdi=5620&_rdoc=15&_acct=C000050221&_version=1&_userid=10&md5=2f417f03979497d537f4483d920ac441" title="Click to view the MathML source" alt="Click to view the MathML source">M is nonsingular. Basic iterative methods such as Jacobi or Gauss–Seidel define the iterative scheme for matrices that have no zeros along its main diagonal.