A fully parallel method for the singular eigenvalue problem

✍ Scribed by Kuiyuan Li; J. Uvah; Shengbian Zhao

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 302 KB
• Volume: 49
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2004.03.017

✦ Synopsis

In this paper, a fully parallel method for finding some or all finite eigenvalues of a real symmetric matrix pencil (A, B) is presented, where A is a symmetric tridiagonal matrix and B is a diagonal matrix with bl > 0 and bi :> 0, i = 2,3,...,n. The method is based on the homotopy continuation with rank 2 perturbation. It is shown that there are exactly m disjoint, smooth homotopy paths connecting the trivial eigenvalues to the desired eigenvalues, where m is the number of finite eigenvalues of (A, B). It is Mso shown that the homotopy curves are monotonic and easy to follow.