Accurate bidiagonal decomposition of totally positive h-Bernstein-Vandermonde matrices and applications

An algorithm for the computation of the bidiagonal decomposition of strictly totally positive h-Bernstein-Vandermonde matrices is presented. These matrices are collocation matrices of h-Bernstein bases (a generalization of the Bernstein basis) of the space of polynomials of degree less than or equal...

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Detalles Bibliográficos
Autores: Marco García, Ana|||0000-0003-4662-6327, Martínez Fernández de las Heras, José Javier|||0000-0002-8322-0361, Viaña Fernández, Raquel|||0000-0001-5484-9104
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/63577
Acceso en línea:http://hdl.handle.net/10017/63577
https://dx.doi.org/10.1016/j.laa.2019.06.003
Access Level:acceso abierto
Palabra clave:Vandermonde matrix
h-Bernstein basis
Totally positive matrix
Neville elimination
Bidiagonal decomposition
High relative accuracy
Matemáticas
Mathematics
Descripción
Sumario:An algorithm for the computation of the bidiagonal decomposition of strictly totally positive h-Bernstein-Vandermonde matrices is presented. These matrices are collocation matrices of h-Bernstein bases (a generalization of the Bernstein basis) of the space of polynomials of degree less than or equal to n. The algorithm is fast (its computational complexity is O (n2) and has high relative accuracy. The computation of this bidiagonal decomposition is used as the initial stage for the accurate and efficient solution of several linear algebra problems with these matrices: linear system solving, eigenvalue computation and inverse computation. Numerical experiments are also included.