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...
| Autores: | , , |
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| 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 |
| 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. |
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