A family of least change diagonally quasi-Newton methods for nonlinear equations
A new family of least-change weak-secant methods for solving systems of nonlinear algebraic equations is introduced. This class of methods belongs to that of quasi-Newton family, except for which the approximation to the Jacobian, at each step, is updated by means of a diagonal matrix. The approa...
| Main Authors: | , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2010
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/9327/1/ID%209327.pdf |
| _version_ | 1825944565272543232 |
|---|---|
| author | Leong, Wah June Abu Hassan, Malik |
| author_facet | Leong, Wah June Abu Hassan, Malik |
| author_sort | Leong, Wah June |
| collection | UPM |
| description | A new family of least-change weak-secant methods for solving systems of nonlinear algebraic
equations is introduced. This class of methods belongs to that of quasi-Newton
family, except for which the approximation to the Jacobian, at each step, is updated by
means of a diagonal matrix. The approach underlying such approximation is based upon
the commonly used least change updating strategy with the added restriction that full
matrices are replaced by diagonal matrices. Using some appropriate matrix norms, some
members of this family are introduced. Convergence results are proved, and particular
members of the family that seem to be of practical usefulness are also considered. |
| first_indexed | 2024-03-06T07:17:52Z |
| format | Conference or Workshop Item |
| id | upm.eprints-9327 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:17:52Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | upm.eprints-93272015-01-21T07:33:17Z http://psasir.upm.edu.my/id/eprint/9327/ A family of least change diagonally quasi-Newton methods for nonlinear equations Leong, Wah June Abu Hassan, Malik A new family of least-change weak-secant methods for solving systems of nonlinear algebraic equations is introduced. This class of methods belongs to that of quasi-Newton family, except for which the approximation to the Jacobian, at each step, is updated by means of a diagonal matrix. The approach underlying such approximation is based upon the commonly used least change updating strategy with the added restriction that full matrices are replaced by diagonal matrices. Using some appropriate matrix norms, some members of this family are introduced. Convergence results are proved, and particular members of the family that seem to be of practical usefulness are also considered. 2010 Conference or Workshop Item NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/9327/1/ID%209327.pdf Leong, Wah June and Abu Hassan, Malik (2010) A family of least change diagonally quasi-Newton methods for nonlinear equations. In: The 8th International Conference on Optimization: Techniques and Applications (ICOTA 8), 10-13 Dec. 2010, Shanghai, China. (pp. 315-316). Equations Algorithms |
| spellingShingle | Equations Algorithms Leong, Wah June Abu Hassan, Malik A family of least change diagonally quasi-Newton methods for nonlinear equations |
| title | A family of least change diagonally quasi-Newton methods for nonlinear equations |
| title_full | A family of least change diagonally quasi-Newton methods for nonlinear equations |
| title_fullStr | A family of least change diagonally quasi-Newton methods for nonlinear equations |
| title_full_unstemmed | A family of least change diagonally quasi-Newton methods for nonlinear equations |
| title_short | A family of least change diagonally quasi-Newton methods for nonlinear equations |
| title_sort | family of least change diagonally quasi newton methods for nonlinear equations |
| topic | Equations Algorithms |
| url | http://psasir.upm.edu.my/id/eprint/9327/1/ID%209327.pdf |
| work_keys_str_mv | AT leongwahjune afamilyofleastchangediagonallyquasinewtonmethodsfornonlinearequations AT abuhassanmalik afamilyofleastchangediagonallyquasinewtonmethodsfornonlinearequations AT leongwahjune familyofleastchangediagonallyquasinewtonmethodsfornonlinearequations AT abuhassanmalik familyofleastchangediagonallyquasinewtonmethodsfornonlinearequations |