The eigenvalue problem for infinite complex symmetric tridiagonal matrices with application
type: Item
instance of: scholarly article
title: The eigenvalue problem for infinite complex symmetric tridiagonal matrices with application
zbMATH Open document ID: 0857.15001
DOI: 10.1016/0024-3795(95)00699-0
author: Yasuhiko Ikebe
author: Nobuyoshi Asai
author: Yoshinori Miyazaki
author: Dengsheng Cai
published in: Linear Algebra and its Applications
publication date: 1997-03-11T00:00:00Z
review text: The authors prove that eigenvalues of complex symmetric tridiagonal matrices with bounded off-main diagonal entries and main diagonal entries approaching infinity, are approximated by the eigenvalues of finite principal submatrices under a few hypotheses. The eigenvalue has to be simple, the inner product of the eigenvector with itself (complex bilinear inner product) is nonzero, and a ratio involving it has to approach zero. Applications to the Mathieu equation are given.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 931901
zbMATH Keywords: eigenvalue approximation
zbMATH Keywords: eigenvalues
zbMATH Keywords: complex symmetric tridiagonal matrices
zbMATH Keywords: eigenvector
zbMATH Keywords: Mathieu equation
reviewed by: Ki Hang Kim
describes a project that uses: LAPACK
describes a project that uses: EISPACK
MaRDI profile type: Publication
full work available at URL: 0024-3795(95)00699-0
OpenAlex ID: W2004556758
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description: scientific article; zbMATH DE number 931901