A new algorithm on the inverse eigenvalue problem for double dimensional Jacobi matrices
type: Item
instance of: scholarly article
title: A new algorithm on the inverse eigenvalue problem for double dimensional Jacobi matrices
zbMATH Open document ID: 1251.65051
author: Xiaoqian Wu
author: Erxiong Jiang
published in: Linear Algebra and its Applications
publication date: 2012-08-27T00:00:00Z
review text: Some properties of eigenvalues and eigenvectors of Jacobi matrices are studied. A new algorithm for reconstructing a \(2n\)-th order Jacobi matrix \(J_{2n}\) with a given \(n\)th order leading principal submatrix \(J_{n}\) and with all eigenvalues of \(J_{2n}\) is proposed. This algorithm needs to compute the eigenvalues of the \(n\)th order tailing principal submatrix \(J_{n+1,2n}\) and the first components of the unit eigenvectors of \(J_{n+1,2n}\). The method avoids computing the coefficients of the characteristic polynomial for getting the eigenvalues of \(J_{n+1,2n}\). Some numerical results are presented.
Mathematics Subject Classification ID: 65F18
zbMATH DE Number: 6072629
zbMATH Keywords: symmetric tridiagonal matrix
zbMATH Keywords: Jacobi matrix
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: double dimension problem
zbMATH Keywords: eigenvectors
zbMATH Keywords: algorithm
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.laa.2012.05.009
OpenAlex ID: W1991596020
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DOI: 10.1016/J.LAA.2012.05.009
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description: scientific article; zbMATH DE number 6072629