New stopping criteria for iterative root finding
A set of simple stopping criteria is presented, which improve the efficiency of iterative root finding by terminating the iterations immediately when no further improvement of the roots is possible. The criteria use only the function evaluations already needed by the root finding procedure to which...
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| Format: | Article |
| Language: | English |
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The Royal Society
2014-01-01
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| Series: | Royal Society Open Science |
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| Online Access: | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140206 |
| _version_ | 1828496515898802176 |
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| author | Jorgen L. Nikolajsen |
| author_facet | Jorgen L. Nikolajsen |
| author_sort | Jorgen L. Nikolajsen |
| collection | DOAJ |
| description | A set of simple stopping criteria is presented, which improve the efficiency of iterative root finding by terminating the iterations immediately when no further improvement of the roots is possible. The criteria use only the function evaluations already needed by the root finding procedure to which they are applied. The improved efficiency is achieved by formulating the stopping criteria in terms of fractional significant digits. Test results show that the new stopping criteria reduce the iteration work load by about one-third compared with the most efficient stopping criteria currently available. This is achieved without compromising the accuracy of the extracted roots. |
| first_indexed | 2024-12-11T12:31:09Z |
| format | Article |
| id | doaj.art-41c0cf45ea3b43eaa8656d63c56881a7 |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-12-11T12:31:09Z |
| publishDate | 2014-01-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-41c0cf45ea3b43eaa8656d63c56881a72022-12-22T01:07:14ZengThe Royal SocietyRoyal Society Open Science2054-57032014-01-011210.1098/rsos.140206140206New stopping criteria for iterative root findingJorgen L. NikolajsenA set of simple stopping criteria is presented, which improve the efficiency of iterative root finding by terminating the iterations immediately when no further improvement of the roots is possible. The criteria use only the function evaluations already needed by the root finding procedure to which they are applied. The improved efficiency is achieved by formulating the stopping criteria in terms of fractional significant digits. Test results show that the new stopping criteria reduce the iteration work load by about one-third compared with the most efficient stopping criteria currently available. This is achieved without compromising the accuracy of the extracted roots.https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140206stopping criteriaroot findingfractional significant digits |
| spellingShingle | Jorgen L. Nikolajsen New stopping criteria for iterative root finding Royal Society Open Science stopping criteria root finding fractional significant digits |
| title | New stopping criteria for iterative root finding |
| title_full | New stopping criteria for iterative root finding |
| title_fullStr | New stopping criteria for iterative root finding |
| title_full_unstemmed | New stopping criteria for iterative root finding |
| title_short | New stopping criteria for iterative root finding |
| title_sort | new stopping criteria for iterative root finding |
| topic | stopping criteria root finding fractional significant digits |
| url | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140206 |
| work_keys_str_mv | AT jorgenlnikolajsen newstoppingcriteriaforiterativerootfinding |