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| Name: | ||
| Miloslav Znojil | ||
| Reviewer number: | ||
| 9689 | ||
| Email: | ||
| znojil@ujf.cas.cz | ||
| Item's zbl-Number: | ||
| DE 018 487 390 | ||
| Author(s): | ||
| Golub, Gene H.; Ye, Qiang: | ||
| Shorttitle: | ||
| An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems | ||
| Source: | ||
| SIAM J. Sci. Comput. 24, No. 1, 312 - 334 (2002) | ||
| Classification: | ||
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| Primary Classification: | ||
| Secondary Classification: | ||
| Keywords: | ||
| pencil problem; Krylov basis; iteration method; convergence analysis; preconditioning scheme; no inversion | ||
| Review: | ||
| After one replaces ``inverse free" in the title by ``inverse-free", the subject of this paper becomes clear: Its authors mean ``no inversion of B > 0 or shifted A" and recommend pre-conditioning. The latter is derived from convergence theory, and the key difference from the Lanczos method lies in the use of a ``shifted-A orthogonality" concept. The merits of the new inner/outer iteration algorithm are seen in its simplified form and, when compared with several Jacobi-Davidson-style approaches, in a fixed cost per outer iteration. Its present limitations to the symmetric generalized eigenvalue problem and to the single-item-per-iteration result seem just temporary. | ||
| Remarks to the editors: | ||