61590 20190709135426.0 doi 10.1016/j.laa.2016.12.003 sideral 97529 ART-2017-97529 eng Marco, Ana Accurate bidiagonal decomposition of totally positive Cauchy-Vandermonde matrices and applications 2017 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/MICINN/MTM2015-65433-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.972 2017 MATHEMATICS 76 / 309 = 0.246 2017 Q1 T1 MATHEMATICS, APPLIED 125 / 252 = 0.496 2017 Q2 T2 0.994 2017 Algebra and Number Theory 2017 Q1 Discrete Mathematics and Combinatorics 2017 Q1 Geometry and Topology 2017 Q2 Numerical Analysis 2017 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Martínez, José-Javier (orcid)0000-0002-1340-0666 Peña, Juan Manuel Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 517 (2017), 63-84 Linear algebra appl. LINEAR ALGEBRA AND ITS APPLICATIONS 0024-3795 389660 http://zaguan.unizar.es/record/61590/files/texto_completo.pdf Preprint 63192 http://zaguan.unizar.es/record/61590/files/texto_completo.jpg?subformat=icon icon Preprint oai:zaguan.unizar.es:61590 articulos driver 2019-07-09-11:29:15 ARTICLE