A family of least change diagonally quasi-Newton methods for nonlinear equations

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 December 2010, Shanghai, China.

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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.

Item Type:Conference or Workshop Item (Paper)
Keyword:nonlinear equations, quasi-Newton methods, weak-secant updates, diagonal approximation
Faculty or Institute:Faculty of Science
ID Code:9327
Deposited By: Samsida Samsudin
Deposited On:24 Jan 2011 09:10
Last Modified:08 Nov 2013 04:26

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