Verified Computation of Eigenpairs in the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils

作     者：Shinya MIYAJIMA Shinya MIYAJIMA

作者机构：Faculty of Science and Engineering Iwate University 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))

年 卷 期：2020年第40卷第1期

页      面：73-86页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Partially Supported by JSPS KAKENHI(Grant No.JP16K05270) the Research Institute for Mathematical Sciences,a Joint Usage/Research Center located in Kyoto University 

主　　题：generalized eigenvalue problem nonsquare pencil invariant subspace verified numerical computation 

摘      要：Consider an optimization problem arising from the generalized eigenvalue problem Ax = λBx, where A, B ∈ C;and m n. Ito et al. showed that the optimization problem can be solved by utilizing right singular vectors of C := [B, A]. In this paper, we focus on computing intervals containing the solution. When some singular values of C are multiple or nearly multiple, we can enclose bases of corresponding invariant subspaces of C;C, where C;denotes the conjugate transpose of C, but cannot enclose the corresponding right singular *** purpose of this paper is to prove that the solution can be obtained even when we utilize the bases instead of the right singular vectors. Based on the proved result, we propose an algorithm for computing the intervals. Numerical results show property of the algorithm.