Modifications of the continuation method for the solution of systems of nonlinear equations
Modifications are proposed to the Davidenko-Broyden algorithm for the solution of a system of nonlinear equations. The aim of the modifications is to reduce the overall number of function evaluations by limiting the number of function evaluations for any one subproblem. To do this alterations are ma...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000260 |
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| _version_ | 1832549248398262272 |
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| author | G. R. Lindfield D. C. Simpson |
| author_facet | G. R. Lindfield D. C. Simpson |
| author_sort | G. R. Lindfield |
| collection | DOAJ |
| description | Modifications are proposed to the Davidenko-Broyden algorithm for the solution of a system of nonlinear equations. The aim of the modifications is to reduce the overall number of function evaluations by limiting the number of function evaluations for any one subproblem. To do this alterations are made to the strategy used in determining the subproblems to be solved. The modifications are compared with other methods for a wide range of test problems, and are shown to significantly reduce the number of function evaluations for the difficult problems. For the easier problems the modified method is equivalent to the Davidenko-Broyden algorithm. |
| format | Article |
| id | doaj-art-a092247d45934748ba7b7f7990bdf7fa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a092247d45934748ba7b7f7990bdf7fa2025-02-03T06:11:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012229930810.1155/S0161171279000260Modifications of the continuation method for the solution of systems of nonlinear equationsG. R. Lindfield0D. C. Simpson1Computer Centre, The University of Aston in Birmingham, 15 Coleshill Street, Birmingham B4 7PA, United KingdomComputer Centre, The University of Aston in Birmingham, 15 Coleshill Street, Birmingham B4 7PA, United KingdomModifications are proposed to the Davidenko-Broyden algorithm for the solution of a system of nonlinear equations. The aim of the modifications is to reduce the overall number of function evaluations by limiting the number of function evaluations for any one subproblem. To do this alterations are made to the strategy used in determining the subproblems to be solved. The modifications are compared with other methods for a wide range of test problems, and are shown to significantly reduce the number of function evaluations for the difficult problems. For the easier problems the modified method is equivalent to the Davidenko-Broyden algorithm.http://dx.doi.org/10.1155/S0161171279000260Davidenko-Broyden algorithmnonlinear equationsnumerical solutions. |
| spellingShingle | G. R. Lindfield D. C. Simpson Modifications of the continuation method for the solution of systems of nonlinear equations International Journal of Mathematics and Mathematical Sciences Davidenko-Broyden algorithm nonlinear equations numerical solutions. |
| title | Modifications of the continuation method for the solution of systems of nonlinear equations |
| title_full | Modifications of the continuation method for the solution of systems of nonlinear equations |
| title_fullStr | Modifications of the continuation method for the solution of systems of nonlinear equations |
| title_full_unstemmed | Modifications of the continuation method for the solution of systems of nonlinear equations |
| title_short | Modifications of the continuation method for the solution of systems of nonlinear equations |
| title_sort | modifications of the continuation method for the solution of systems of nonlinear equations |
| topic | Davidenko-Broyden algorithm nonlinear equations numerical solutions. |
| url | http://dx.doi.org/10.1155/S0161171279000260 |
| work_keys_str_mv | AT grlindfield modificationsofthecontinuationmethodforthesolutionofsystemsofnonlinearequations AT dcsimpson modificationsofthecontinuationmethodforthesolutionofsystemsofnonlinearequations |