Weighted FOM-inverse vector iteration method for computing a few smallest (largest) eigenvalues of pair (A, B)

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• 作者：H. Saberi Najafi ; A. Refahi ; M. Akbari
• 关键词：Generalized eigenvalue ; Arnoldi ; Symmetric ; Positive definite ; Weighted FOM
• 刊名：Applied Mathematics and Computation
• 出版年：2007
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 September 2007
• 卷：192
• 期：1
• 页码：239-246
• 文件大小：207 K

摘要

The generalized eigenvalue problem href="/science?_ob=MathURL&_method=retrieve&_udi=B6TY8-4N987X7-1&_mathId=mml6&_user=10&_cdi=5612&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=3b65a7aa0fb0bd6391e7af338d16bf09" title="Click to view the MathML source">AX=λBX has special properties when (A, B) is a symmetric and positive definite pair.

We have recently developed a new method for computing a few smallest (largest) eigenvalues of a symmetric positive definite problem href="/science?_ob=MathURL&_method=retrieve&_udi=B6TY8-4N987X7-1&_mathId=mml7&_user=10&_cdi=5612&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=dd200201159c8110422e27ea5a9349f1" title="Click to view the MathML source">AX=λBX [H. Saberi Najafi, A. Refahi, FOM-inverse vector iteration method for computing a few smallest (largest) eigenvalues of pair (A, B), Appl. Math., in press] the method used three parameters, which are weighted Arnoldi, Inner and outer iterations parameters. In this article those parameters have been optimized to increase the speed of convergence. The method has been tested by some numerical examples.