A finite-step construction of totally nonnegative matrices with specified eigenvalues
type: Item
instance of: scholarly article
title: A finite-step construction of totally nonnegative matrices with specified eigenvalues
zbMATH Open document ID: 1334.65074
author: Kanae Akaiwa
author: Yoshimasa Nakamura
author: Masashi Iwasaki
author: Hisayoshi Tsutsumi
author: Koichi Kondo
published in: Numerical Algorithms
publication date: 2015-11-17T00:00:00Z
review text: The authors focus on an inverse eigenvalue problem related to banded totally nonnegative (TN) matrices, which can be expressed by products of other bidiagonal TN matrices. Following an approach already presented in the literature, the authors study the eigenvalue problem from the point of view of the discrete hungry Toda (dhToda) equation. First, the determinant solution to the dhToda equation with suitable boundary conditions is presented. Then, it is shown that the characteristic polynomials of the banded TN matrices are related to the determinant solution. At last, an algorithm for constructing banded TN matrices with specified eigenvalues is given and a numerical example referring to \( 5\times 5\) TN matrices is reported.
Mathematics Subject Classification ID: 65F18
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 6510056
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: discrete hungry Toda equation
zbMATH Keywords: banded totally nonnegative matrices
zbMATH Keywords: algorithm
zbMATH Keywords: numerical example
reviewed by: Raffaella Pavani
describes a project that uses: gmp
MaRDI profile type: Publication
full work available at URL: s11075-015-9957-x
OpenAlex ID: W2086231554
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DOI: 10.1007/S11075-015-9957-X
description: scientific article; zbMATH DE number 6510056