Affiliation:
1. Departamento de Matemática Aplicada/IUMA Universidad de Zaragoza Zaragoza Spain
Abstract
AbstractIn this article, it is proved that Gram matrices of totally positive bases of the space of polynomials of a given degree on a compact interval are totally positive. Conditions to guarantee computations to high relative accuracy with those matrices are also obtained. Furthermore, a fast and accurate algorithm to compute the bidiagonal factorization of Gram matrices of the Said‐Ball bases is obtained and used to compute to high relative accuracy their singular values and inverses, as well as the solution of some linear systems associated with these matrices. Numerical examples are included.
Funder
Gobierno de Aragón
Agencia Estatal de Investigación
Subject
Applied Mathematics,Algebra and Number Theory