GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems
| dc.contributor.author | Greenbaum, Anne | en_US |
| dc.contributor.author | Trefethen, Lloyd N. | en_US |
| dc.date.accessioned | 2007-04-03T14:42:42Z | |
| dc.date.available | 2007-04-03T14:42:42Z | |
| dc.date.issued | 1992-06 | en_US |
| dc.description.abstract | The GMRES and Arnoldi algorithms, which reduce to the CR and Lanczos algorithms in the symmetric case, both minimize ||p(A)b|| over polynomials p of degree n. The difference is that p is nor- malized at z=0 for GMRES and at z=infinity for Arnoldi. Analogous "ideal GMRES" and "ideal Arnoldi" problems are obtained if one removes b from the discussion and minimizes ||p(A)|| instead. Investigation of these true and ideal approximation problems gives insight into how fast GMRES converges and how the Arnoldi iteration locates eigenvalues. | en_US |
| dc.format.extent | 195079 bytes | |
| dc.format.extent | 573011 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.citation | http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/92-096 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/5473 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Cornell University | en_US |
| dc.subject | theory center | en_US |
| dc.title | GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems | en_US |
| dc.type | technical report | en_US |