Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
| dc.contributor.author | Lehoucq, R.B. | |
| dc.contributor.author | Sorensen, Danny C. | |
| dc.date.accessioned | 2018-06-18T17:41:50Z | |
| dc.date.available | 2018-06-18T17:41:50Z | |
| dc.date.issued | 1994-09 | |
| dc.date.note | September 1994 (Revised February 1995) | |
| dc.description.abstract | A deflation procedure is introduced that is designed to improve convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at different rates. A numerically stable deflation scheme is introduced that implicitly deflates the converged approximations from the iteration. We present two forms of implicit deflation. The first, a locking operation, decouples converged Ritz values and associated vectors from the active part of the iteration. The second, a purgingoperation, removes unwanted but converged Ritz pairs. Convergence of the iteration is improved and a reduction in computational effort is also achieved. The deflation strategies make it possible to compute multiple or clustered eigenvalues with a single vector restart method. A Block method is not required. These schemes are analyzed with respect to numerical stability and computational results are presented. | |
| dc.format.extent | 38 pp | |
| dc.identifier.citation | Lehoucq, R.B. and Sorensen, Danny C.. "Deflation Techniques for an Implicitly Restarted Arnoldi Iteration." (1994) <a href="https://hdl.handle.net/1911/101832">https://hdl.handle.net/1911/101832</a>. | |
| dc.identifier.digital | TR94-13 | |
| dc.identifier.uri | https://hdl.handle.net/1911/101832 | |
| dc.language.iso | eng | |
| dc.title | Deflation Techniques for an Implicitly Restarted Arnoldi Iteration | |
| dc.type | Technical report | |
| dc.type.dcmi | Text |
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