Bidiagonal decompositions of Vandermonde-type matrices of arbitrary rank

Delgado, Jorge (Universidad de Zaragoza) ; Koev, Plamen ; Marco, Ana ; Martínez, José-Javier ; Peña, Juan Manuel (Universidad de Zaragoza) ; Persson, Per-Olof ; Spasov, Steven

Resumen: We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (-, -) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for nonsingular matrices to matrices of arbitrary rank. For totally nonnegative matrices of the above classes, the new decompositions can be computed efficiently and to high relative accuracy componentwise in floating point arithmetic. In turn, matrix computations (e.g., eigenvalue computation) can also be performed efficiently and to high relative accuracy.

Idioma: Inglés

DOI: 10.1016/j.cam.2023.115064

Año: 2023

Publicado en: Journal of Computational and Applied Mathematics 426 (2023), 115064 [15 pp.]
ISSN: 0377-0427

Factor impacto JCR: 2.1 (2023)

Categ. JCR: MATHEMATICS, APPLIED rank: 53 / 332 = 0.16 (2023) - Q1 - T1

Factor impacto CITESCORE: 5.4 - Computational Mathematics (Q1) - Applied Mathematics (Q1)

Factor impacto SCIMAGO: 0.858 - Computational Mathematics (Q2) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-17R
Financiación: info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00

Tipo y forma: Article (Published version)

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