Error analysis, perturbation theory and applications of the bidiagonal decomposition of rectangular totally-positive h-Bernstein-Vandermonde matrices
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/60006DOI: 10.1016/j.laa.2020.11.015
ISSN: 0024-3795
Publisher
Elsevier
Date
2021-03-15Funders
Agencia Estatal de Investigación
Bibliographic citation
Marco García, A., Martínez Fernández de las Heras, J.J. & Viaña Fernández, R. 2021, “Error analysis, perturbation theory and applications of the bidiagonal decomposition of rectangular totally positive h-Bernstein-Vandermonde matrices”, Linear Algebra and its Applications, vol. 613, pp. 377-392.
Keywords
Vandermonde matrix
h-Bernstein basis
Totally positive matrix
Neville elimination
Bidiagonal decomposition
High relative accuracy
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-096321-B-I00/ES/ANALISIS DE LA REPRESENTACION DE CURVAS Y SUPERFICIES, CALCULOS PRECISOS CON MATRICES ESTRUCTURADAS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.laa.2020.11.015Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2020 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
A fast and accurate algorithm to compute the bidiagonal decomposition of rectangular totally positive h-Bernstein-Vandermonde matrices is presented. The error analysis of the algorithm and the perturbation theory for the bidiagonal decomposition of totally positive h-Bernstein-Vandermonde matrices are addressed. The computation of this bidiagonal decomposition is used as the first step for the accurate and efficient computation of the singular values of rectangular totally positive h-Bernstein-Vandermonde matrices and for solving least squares problems whose coefficient matrices are such matrices.
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