Constructing symmetric nonnegative matrices via the fast Fourier transform
type: Item
instance of: scholarly article
title: Constructing symmetric nonnegative matrices via the fast Fourier transform
zbMATH Open document ID: 1052.65028
DOI: 10.1016/S0898-1221(03)00145-7
author: Oscar Rojo
author: Héctor Rojo
publication date: 2004-08-06T00:00:00Z
review text: Given a set of real numbers \(\sigma = \{\lambda_1, \lambda_2, \dots, \lambda_n\}\), the authors propose a new method for constructing a real \(n\times n\) symmetric matrix \(S\) with eigenvalues \(\sigma\). The proposed method proceeds by constructing a real and symmetric circulant matrix \(C\) of double dimension so that its (double) eigenvalues are given by \(\tilde \sigma = \{\mu, \lambda_2, \dots, \lambda_n\}\), where \(\mu = - (\lambda_2 + \cdots + \lambda_n)\). Then, after a simple block diagonalization of \(C\), a symmetric \(n \times n\) matrix \(\tilde S\) having eigenvalues \(\tilde \sigma\) is obtained as one of the diagonal blocks. Finally, the matrix \(S\) is constructed from a certain rank-one correction of \(\tilde S\). In the second part of the paper, the authors prove several sufficient conditions under which their method produces an irreducible nonnegative matrix \(S\).
reviewed by: Daniel Kressner
Mathematics Subject Classification ID: 65F18
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 2082288
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: circulant matrix
zbMATH Keywords: stochastic
zbMATH Keywords: matrix
zbMATH Keywords: symmetric matrix
zbMATH Keywords: persymmetric matrix
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2082288