Basis selection in LOBPCG
The purpose of our paper is to discuss basis selection for Knyazev’s locally optimal block preconditioned conjugate gradient (LOBPCG) method. An inappropriate choice of basis can lead to ill-conditioned Gram matrices in the Rayleigh–Ritz analysis that can delay convergence or produce inaccurate eige...
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| Veröffentlicht in: | Journal of computational physics 2006-10, Vol.218 (1), p.324-332 |
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| container_title | Journal of computational physics |
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| creator | Hetmaniuk, U. Lehoucq, R. |
| description | The purpose of our paper is to discuss basis selection for Knyazev’s locally optimal block preconditioned conjugate gradient (LOBPCG) method. An inappropriate choice of basis can lead to ill-conditioned Gram matrices in the Rayleigh–Ritz analysis that can delay convergence or produce inaccurate eigenpairs. We demonstrate that the choice of basis is not merely related to computing in finite precision arithmetic. We propose a representation that maintains orthogonality of the basis vectors and so has excellent numerical properties. |
| doi_str_mv | 10.1016/j.jcp.2006.02.007 |
| format | Article |
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| ispartof | Journal of computational physics, 2006-10, Vol.218 (1), p.324-332 |
| issn | 0021-9991 1090-2716 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Blocking Computation Computational techniques Convergence Delay Exact sciences and technology LOBPCG Mathematical analysis Mathematical methods in physics Optimization Orthonormalization Physics Preconditioned eigensolver Representations Symmetric generalized eigenvalue problem Vectors (mathematics) |
| title | Basis selection in LOBPCG |
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