Parallel iterative refinement in polynomial eigenvalue problems
Methods for the polynomial eigenvalue problem sometimes need to be followed by an iterative refinement process to improve the accuracy of the computed solutions. This can be accomplished by means of a Newton iteration tailored to matrix polynomials. The computational cost of this step is usually hig...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/84108 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/84108 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomial eigenvalue problems Iterative refinement Invariant pairs Parallel computing CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL |
| Sumario: | Methods for the polynomial eigenvalue problem sometimes need to be followed by an iterative refinement process to improve the accuracy of the computed solutions. This can be accomplished by means of a Newton iteration tailored to matrix polynomials. The computational cost of this step is usually higher than the cost of computing the initial approximations, due to the need of solving multiple linear systems of equations with a bordered coefficient matrix. An effective parallelization is thus important, and we propose different approaches for the message-passing scenario. Some schemes use a subcommunicator strategy in order to improve the scalability whenever direct linear solvers are used. We show performance results for the various alternatives implemented in the context of SLEPc, the Scalable Library for Eigenvalue Problem Computations. |
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