Bidiagonal decompositions of Vandermonde-type matrices of arbitrary rank

We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for nonsingular matrices to matrices of arbitrary rank. For totall...

ver descrição completa

Detalhes bibliográficos
Autores: Delgado, Jorge, Koev, Plamen, Marco García, Ana|||0000-0003-4662-6327, Martínez Fernández de las Heras, José Javier|||0000-0002-8322-0361, Peña Ferrández, Juan Manuel, Persson, Per-Oloff, Spasov, Steven
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/60008
Acesso em linha:http://hdl.handle.net/10017/60008
https://dx.doi.org/10.1016/j.cam.2023.115064
Access Level:acceso abierto
Palavra-chave:Vandermonde matrix
Totally nonnegative matrix
Bidiagonal decomposition
Eigenvalue
Matemáticas
Mathematics
Descrição
Resumo:We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) 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.