Factorizations and Accurate Computations with Min and Max Matrices

Khiar, Yasmina (Universidad de Zaragoza) ; Mainar, Esmeralda (Universidad de Zaragoza) ; Royo-Amondarain, Eduardo (Universidad de Zaragoza)

Resumen: Min and max matrices are structured matrices that appear in diverse mathematical and computational applications. Their inherent structures facilitate highly accurate numerical solutions to algebraic problems. In this research, the total positivity of generalized Min and Max matrices is characterized, and their bidiagonal factorizations are derived. It is also demonstrated that these decompositions can be computed with high relative accuracy (HRA), enabling the precise computations of eigenvalues and singular values and the solution of linear systems. Notably, the discussed approach achieves relative errors on the order of the unit roundoff, even for large and ill-conditioned matrices. To illustrate the exceptional accuracy of this method, numerical experiments on quantum extensions of Min and L-Hilbert matrices are presented, showcasing their superior precisions compared to those of standard computational techniques.

Idioma: Inglés

DOI: 10.3390/sym17050684

Año: 2025

Publicado en: Symmetry 17, 5 (2025), 684 [13 pp.]
ISSN: 2073-8994

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T

Tipo y forma: Article (Published version)

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