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: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2010
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/9327/1/ID%209327.pdf |
| Summary: | 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. |
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