A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system

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• 作者：Kazuki Maeda ; ^{kmaeda@kmaeda.net" class="auth_mail" title="E-mail the corresponding author} ; Satoshi Tsujimoto ^{tujimoto@i.kyoto-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：37K10 ; 37K40 ; 42C05 ; 65F15
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：300
• 期：Complete
• 页码：134-154
• 全文大小：610 K

文摘

A generalized eigenvalue algorithm for a certain class of tridiagonal matrix pencils is presented. The algorithm appears as the time evolution equation of a nonautonomous discrete integrable system associated with a polynomial sequence which has some orthogonality on the support set of the zeros of the characteristic polynomial for a tridiagonal matrix pencil. The convergence of the algorithm is discussed by using the solution to the initial value problem for the corresponding discrete integrable system.