Numerical stability of iterative refinement with a relaxation for linear systems
Stability analysis of Wilkinson's iterative refinement with a relaxation IR(omega) for solving linear systems is given. It extends existing results for omega=1, i.e., for Wilkinson's iterative refinement. We assume that all computations are performed in fixed (working) precision arithmetic...
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| creator | Smoktunowicz, Alicja Kierzkowski, Jakub Wrobel, Iwona |
| description | Stability analysis of Wilkinson's iterative refinement with a relaxation
IR(omega) for solving linear systems is given. It extends existing results for
omega=1, i.e., for Wilkinson's iterative refinement. We assume that all
computations are performed in fixed (working) precision arithmetic. Numerical
tests were done in MATLAB to illustrate our theoretical results. A particular
emphasis is given on convergence of iterative refinement with a relaxation. Our
tests confirm that the choice omega=1 is the best choice from the point of
numerical stability. |
| doi_str_mv | 10.48550/arxiv.1512.04246 |
| format | Article |
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IR(omega) for solving linear systems is given. It extends existing results for
omega=1, i.e., for Wilkinson's iterative refinement. We assume that all
computations are performed in fixed (working) precision arithmetic. Numerical
tests were done in MATLAB to illustrate our theoretical results. A particular
emphasis is given on convergence of iterative refinement with a relaxation. Our
tests confirm that the choice omega=1 is the best choice from the point of
numerical stability.</description><identifier>DOI: 10.48550/arxiv.1512.04246</identifier><language>eng</language><subject>Mathematics - Numerical Analysis</subject><creationdate>2015-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1512.04246$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1512.04246$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Smoktunowicz, Alicja</creatorcontrib><creatorcontrib>Kierzkowski, Jakub</creatorcontrib><creatorcontrib>Wrobel, Iwona</creatorcontrib><title>Numerical stability of iterative refinement with a relaxation for linear systems</title><description>Stability analysis of Wilkinson's iterative refinement with a relaxation
IR(omega) for solving linear systems is given. It extends existing results for
omega=1, i.e., for Wilkinson's iterative refinement. We assume that all
computations are performed in fixed (working) precision arithmetic. Numerical
tests were done in MATLAB to illustrate our theoretical results. A particular
emphasis is given on convergence of iterative refinement with a relaxation. Our
tests confirm that the choice omega=1 is the best choice from the point of
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IR(omega) for solving linear systems is given. It extends existing results for
omega=1, i.e., for Wilkinson's iterative refinement. We assume that all
computations are performed in fixed (working) precision arithmetic. Numerical
tests were done in MATLAB to illustrate our theoretical results. A particular
emphasis is given on convergence of iterative refinement with a relaxation. Our
tests confirm that the choice omega=1 is the best choice from the point of
numerical stability.</abstract><doi>10.48550/arxiv.1512.04246</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Numerical Analysis |
| title | Numerical stability of iterative refinement with a relaxation for linear systems |
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