A Parallel Implementation of Davidson Methods for Large-Scale Eigenvalue Problems in SLEPc
In the context of large-scale eigenvalue problems, methods of Davidson type such as Jacobi-Davidson can be competitive with respect to other types of algorithms, especially in some particularly difficult situations such as computing interior eigenvalues or when matrix factorization is prohibitive or...
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| Veröffentlicht in: | ACM transactions on mathematical software 2014-02, Vol.40 (2), p.1-29 |
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| creator | ROMERO, Eloy ROMAN, Jose E |
| description | In the context of large-scale eigenvalue problems, methods of Davidson type such as Jacobi-Davidson can be competitive with respect to other types of algorithms, especially in some particularly difficult situations such as computing interior eigenvalues or when matrix factorization is prohibitive or highly inefficient. However, these types of methods are not generally available in the form of high-quality parallel implementations, especially for the case of non-Hermitian eigenproblems. We present our implementation of various Davidson-type methods in SLEPc, the Scalable Library for Eigenvalue Problem Computations. The solvers incorporate many algorithmic variants for subspace expansion and extraction, and cover a wide range of eigenproblems including standard and generalized, Hermitian and non-Hermitian, with either real or complex arithmetic. We provide performance results on a large battery of test problems. |
| doi_str_mv | 10.1145/2543696 |
| format | Article |
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| subjects | Algebra Algorithms Applied sciences Battery Computation Computer programs Computer science control theory systems Computer systems and distributed systems. User interface Eigenvalues Exact sciences and technology Factorization Information retrieval. Graph Linear and multilinear algebra, matrix theory Mathematics Sciences and techniques of general use Software Solvers Theoretical computing |
| title | A Parallel Implementation of Davidson Methods for Large-Scale Eigenvalue Problems in SLEPc |
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