A new algorithm for computing the inertia of eigenproblems (Ax=λx) and (Ax=λBx)
- 作者：H. Saberi Najafi ; M. Shams Solary
- 关键词：Inertia ; Arnoldi algorithm ; Generalized eigenproblem ; Shift-and-invert ; Gereshgorin ; Block matrix
- 刊名：Applied Mathematics and Computation
- 出版年：2008
- 期刊代码：7_00963003
- 类别：cp
- 出版时间：15 July 2008
- 卷：201
- 期：1-2
- 页码：138-148
- 文件大小：161 K
摘要
The inertia of a href="/science?_ob=MathURL&_method=retrieve&_udi=B6TY8-4R9GGNR-3&_mathId=mml39&_user=1067359&_cdi=5612&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=cbe893cd8202d97e97d07b13e762a794" title="Click to view the MathML source" alt="Click to view the MathML source">n×n complex matrix A, is defined to be an integer triple, href="/science?_ob=MathURL&_method=retrieve&_udi=B6TY8-4R9GGNR-3&_mathId=mml40&_user=1067359&_cdi=5612&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=12e1258fc240558c8db9e38c10fd87ad" title="Click to view the MathML source" alt="Click to view the MathML source">In(A)=(π(A),ν(A),δ(A)), where href="/science?_ob=MathURL&_method=retrieve&_udi=B6TY8-4R9GGNR-3&_mathId=mml41&_user=1067359&_cdi=5612&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=051e41b4bd83f8f0eea85f665cc78c2c" title="Click to view the MathML source" alt="Click to view the MathML source">π(A) is the number of eigenvalues of A with positive real parts, href="/science?_ob=MathURL&_method=retrieve&_udi=B6TY8-4R9GGNR-3&_mathId=mml42&_user=1067359&_cdi=5612&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=383c2490176ab75c0d1c738bf43eda9e" title="Click to view the MathML source" alt="Click to view the MathML source">ν(A) is the number of eigenvalues with negative real parts and href="/science?_ob=MathURL&_method=retrieve&_udi=B6TY8-4R9GGNR-3&_mathId=mml43&_user=1067359&_cdi=5612&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=e7830487999ca6df946e3751a639ff21" title="Click to view the MathML source" alt="Click to view the MathML source">δ(A) is the number of eigenvalues with zero real parts.