Isospectral flows and the inverse eigenvalue problem for Toeplitz matrices
type: Item
instance of: scholarly article
title: Isospectral flows and the inverse eigenvalue problem for Toeplitz matrices
zbMATH Open document ID: 0942.65043
DOI: 10.1016/S0377-0427(99)00193-4
author: Fasma Diele
author: Ivonne Sgura
published in: Journal of Computational and Applied Mathematics
publication date: 2000-08-02T00:00:00Z
review text: The paper is devoted to the inverse eigenvalue problem for Toeplitz matrices that is a real symmetric Toeplitz matrix has to be constructed from prescribed eigenvalues. To solve the problem numerically, a known approach is used, based on isospectral flow solutions, whose equilibria are symmetric Toeplitz matrices. The authors show new properties of the isospectral flow. The case \(n=3\) is studied analytically using a new approach. Global convergence of the iteration process to a regular Toeplitz matrix is proved when starting from a tridiagonal symmetric and centro-symmetric matrix. Numerical experiments confirm the theoretical results and suggest their extension in higher dimension.
Mathematics Subject Classification ID: 65F18
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 1367866
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: isospectral flow
zbMATH Keywords: convergence
zbMATH Keywords: iteration process
zbMATH Keywords: numerical experiments
reviewed by: Neli Dimitrova
MaRDI profile type: Publication
Wikidata QID: Q62027897
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description: scientific article; zbMATH DE number 1367866