Accurate computations with Gram and Wronskian matrices of geometric and Poisson bases

Autor:	Esmeralda Mainar, Juan Manuel Peña, Beatriz Rubio Serrano
Rok vydání:	2022
Předmět:	Computational Mathematics Algebra and Number Theory Applied Mathematics Geometry and Topology Analysis
Zdroj:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 116
ISSN:	1579-1505 1578-7303
DOI:	10.1007/s13398-022-01253-1
Popis:	In this paper we deduce a bidiagonal decomposition of Gram and Wronskian matrices of geometric and Poisson bases. It is also proved that the Gram matrices of both bases are strictly totally positive, that is, all their minors are positive. The mentioned bidiagonal decompositions are used to achieve algebraic computations with high relative accuracy for Gram and Wronskian matrices of these bases. The provided numerical experiments illustrate the accuracy when computing the inverse matrix, the eigenvalues or singular values or the solutions of some linear systems, using the theoretical results.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b51929d1904571dd902ed09f25db897 https://doi.org/10.1007/s13398-022-01253-1 Zobrazit plný text záznamu Full text from SpringerLink