Three Cuts for Accelerated Interval Propagation
This paper addresses the problem of nonlinear multivariate root finding. In an earlier paper we described a system called Newton which finds roots of systems of nonlinear equations using refinements of interval methods. The refinements are inspired by AI constraint propagation techniques. New...
| Main Authors: | , , |
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| Language: | en_US |
| Published: |
2004
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| Online Access: | http://hdl.handle.net/1721.1/6642 |
| _version_ | 1826209116123561984 |
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| author | McAllester, D. Henlenryck, P. Van Kapur, T. |
| author_facet | McAllester, D. Henlenryck, P. Van Kapur, T. |
| author_sort | McAllester, D. |
| collection | MIT |
| description | This paper addresses the problem of nonlinear multivariate root finding. In an earlier paper we described a system called Newton which finds roots of systems of nonlinear equations using refinements of interval methods. The refinements are inspired by AI constraint propagation techniques. Newton is competative with continuation methods on most benchmarks and can handle a variety of cases that are infeasible for continuation methods. This paper presents three "cuts" which we believe capture the essential theoretical ideas behind the success of Newton. This paper describes the cuts in a concise and abstract manner which, we believe, makes the theoretical content of our work more apparent. Any implementation will need to adopt some heuristic control mechanism. Heuristic control of the cuts is only briefly discussed here. |
| first_indexed | 2024-09-23T14:17:29Z |
| id | mit-1721.1/6642 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:17:29Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/66422019-04-11T02:52:39Z Three Cuts for Accelerated Interval Propagation McAllester, D. Henlenryck, P. Van Kapur, T. This paper addresses the problem of nonlinear multivariate root finding. In an earlier paper we described a system called Newton which finds roots of systems of nonlinear equations using refinements of interval methods. The refinements are inspired by AI constraint propagation techniques. Newton is competative with continuation methods on most benchmarks and can handle a variety of cases that are infeasible for continuation methods. This paper presents three "cuts" which we believe capture the essential theoretical ideas behind the success of Newton. This paper describes the cuts in a concise and abstract manner which, we believe, makes the theoretical content of our work more apparent. Any implementation will need to adopt some heuristic control mechanism. Heuristic control of the cuts is only briefly discussed here. 2004-10-08T20:36:08Z 2004-10-08T20:36:08Z 1995-05-01 AIM-1542 http://hdl.handle.net/1721.1/6642 en_US AIM-1542 174936 bytes 310056 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | McAllester, D. Henlenryck, P. Van Kapur, T. Three Cuts for Accelerated Interval Propagation |
| title | Three Cuts for Accelerated Interval Propagation |
| title_full | Three Cuts for Accelerated Interval Propagation |
| title_fullStr | Three Cuts for Accelerated Interval Propagation |
| title_full_unstemmed | Three Cuts for Accelerated Interval Propagation |
| title_short | Three Cuts for Accelerated Interval Propagation |
| title_sort | three cuts for accelerated interval propagation |
| url | http://hdl.handle.net/1721.1/6642 |
| work_keys_str_mv | AT mcallesterd threecutsforacceleratedintervalpropagation AT henlenryckpvan threecutsforacceleratedintervalpropagation AT kapurt threecutsforacceleratedintervalpropagation |