GPU implementation of Krylov solvers for block-tridiagonal eigenvalue problems
In an eigenvalue problem defined by one or two matrices with block-tridiagonal structure, if only a few eigenpairs are required it is interesting to consider iterative methods based on Krylov subspaces, even if matrix blocks are dense. In this context, using the GPU for the associated dense linear a...
| Autores: | , |
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| Tipo de documento: | capítulo de livro |
| Data de publicação: | 2016 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositório: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglês |
| OAI Identifier: | oai:riunet.upv.es:10251/66516 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/66516 |
| Access Level: | Acceso aberto |
| Palavra-chave: | GPU computing Eigenvalue computation Krylov methods Block-tridiagonal linear solvers CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL |
| Resumo: | In an eigenvalue problem defined by one or two matrices with block-tridiagonal structure, if only a few eigenpairs are required it is interesting to consider iterative methods based on Krylov subspaces, even if matrix blocks are dense. In this context, using the GPU for the associated dense linear algebra may provide high performance. We analyze this in an implementation done in the context of SLEPc, the Scalable Library for Eigenvalue Problem Computations. In the case of a generalized eigenproblem or when interior eigenvalues are computed with shift-and-invert, the main computational kernel is the solution of linear systems with a block-tridiagonal matrix. We explore possible implementations of this operation on the GPU, including a block cyclic reduction algorithm. |
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