Error analysis, perturbation theory and applications of the bidiagonal decomposition of rectangular totally-positive h-Bernstein-Vandermonde matrices

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 a...

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Detalles Bibliográficos
Autores: Marco García, Ana|||0000-0003-4662-6327, Martínez Fernández de las Heras, José Javier|||0000-0002-8322-0361, Viaña Fernández, Raquel|||0000-0001-5484-9104
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/60006
Acceso en línea:http://hdl.handle.net/10017/60006
https://dx.doi.org/10.1016/j.laa.2020.11.015
Access Level:acceso abierto
Palabra clave:Vandermonde matrix
h-Bernstein basis
Totally positive matrix
Neville elimination
Bidiagonal decomposition
High relative accuracy
Matemáticas
Mathematics
Descripción
Sumario: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.