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| Name: | ||
| Miloslav Znojil | ||
| Reviewer number: | ||
| 9689 | ||
| Email: | ||
| znojil@ujf.cas.cz | ||
| Item's zbl-Number: | ||
| DE 018 647 897 | ||
| Author(s): | ||
| Dax, Achiya: | ||
| Shorttitle: | ||
| The orthogonal Rayleigh quotient iteration method | ||
| Source: | ||
| Linear Algebra Appl. 358, No. 1-3, 23-43 (2003) | ||
| Classification: | ||
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| Primary Classification: | ||
| Secondary Classification: | ||
| Keywords: | ||
| global inverse iterations; re-orthogonalization; selective orthogonalization; real symmetric band matrices; diagonalization method; error analysis | ||
| Review: | ||
| Under a new name we find here the method of inverse iterations (cf. J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon, Oxford, 1965). The author performs its error analysis and emphasizes that although the ``local" rate of its convergence is cubic, a difficulty may be encountered in a ``global" setting where, in principle, the residual function may possess a saddle point. After one avoids this trap, the efficiency of the algorithm is kept reasonable by performing the necessary re-orthogonalizations ``selectively" and by working with the band matrices possessing a narrow bandwith. | ||
| Remarks to the editors: | ||