Accurate Computations with Generalized Green Matrices

Delgado, Jorge (Universidad de Zaragoza) ; Peña, Guillermo (Universidad de Zaragoza) ; Peña, Juan Manuel (Universidad de Zaragoza)

Resumen: We consider generalized Green matrices that, in contrast to Green matrices, are not necessarily symmetric. In spite of the loss of symmetry, we show that they can preserve some nice properties of Green matrices. In particular, they admit a bidiagonal decomposition. Moreover, for convenient parameters, the bidiagonal decomposition can be obtained efficiently and with high relative accuracy and it can also be used to compute all eigenvalues, all singular values, the inverse, and the solution of some linear system of equations with high relative accuracy. Numerical examples illustrate the high accuracy of the performed computations using the bidiagonal decompositions. Finally, nonsingular and totally positive generalized Green matrices are characterized.

Idioma: Inglés

DOI: 10.3390/sym16081004

Año: 2024

Publicado en: Symmetry 16, 8 (2024), 1004 [12 pp.]
ISSN: 2073-8994

Factor impacto JCR: 2.2 (2024)

Categ. JCR: MULTIDISCIPLINARY SCIENCES rank: 54 / 135 = 0.4 (2024) - Q2 - T2

Factor impacto SCIMAGO: 0.467 - Chemistry (miscellaneous) (Q2) - Physics and Astronomy (miscellaneous) (Q2) - Mathematics (miscellaneous) (Q2) - Computer Science (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2020-112773GB-I00
Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/DGA/S39-23R
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)
Área (Departamento): Área Fund. Análisis Económico (Dpto. Análisis Económico)