Accurate bidiagonal decomposition of totally positive Cauchy-Vandermonde matrices and applications

Marco, Ana ; Martínez, José-Javier ; Peña, Juan Manuel (Universidad de Zaragoza)

Resumen: Cauchy–Vandermonde matrices play a fundamental role in rational interpolation theory and in other fields. When all their corresponding nodes are different and positive and all poles are different and negative and follow adequate orderings, these matrices are totally positive. In this paper we provide fast algorithms for computing bidiagonal factorizations of these matrices and their inverses with high relative accuracy. These algorithms can be used to solve with high relative accuracy other algebraic problems, such as the computation of all singular values, all eigenvalues or the solution of certain linear systems. The error analysis of the algorithm for computing the bidiagonal factorization and the corresponding perturbation theory are also performed.

Idioma: Inglés

DOI: 10.1016/j.laa.2016.12.003

Año: 2017

Publicado en: LINEAR ALGEBRA AND ITS APPLICATIONS 517 (2017), 63-84
ISSN: 0024-3795

Factor impacto JCR: 0.972 (2017)

Categ. JCR: MATHEMATICS rank: 76 / 309 = 0.246 (2017) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 125 / 252 = 0.496 (2017) - Q2 - T2

Factor impacto SCIMAGO: 0.994 - Algebra and Number Theory (Q1) - Discrete Mathematics and Combinatorics (Q1) - Geometry and Topology (Q2) - Numerical Analysis (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2015-65433-P

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)