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

Mainar, E. (Universidad de Zaragoza) ; Peña, J. M. (Universidad de Zaragoza) ; Rubio, B. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s13398-022-01253-1

Año: 2022

Publicado en: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 116 (2022), 126 [22 pp.]
ISSN: 1578-7303

Factor impacto JCR: 2.9 (2022)

Categ. JCR: MATHEMATICS rank: 15 / 329 = 0.046 (2022) - Q1 - T1

Factor impacto CITESCORE: 4.9 - Mathematics (Q1)

Factor impacto SCIMAGO: 0.933 - Algebra and Number Theory (Q1) - Analysis (Q1) - Geometry and Topology (Q1) - Computational Mathematics (Q1) - Applied Mathematics (Q1)

Tipo y forma: Artículo (Versión definitiva)

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