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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 Dec. 2010, Shanghai, China. (pp. 315-316).


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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Additional Metadata

Item Type: Conference or Workshop Item (Paper)
Subject: Equations
Subject: Algorithms
Divisions: Faculty of Science
Keywords: Nonlinear equations; Quasi-Newton methods; Weak-secant updates; Diagonal approximation
Depositing User: Samsida Samsudin
Date Deposited: 24 Jan 2011 09:10
Last Modified: 21 Jan 2015 07:33
URI: http://psasir.upm.edu.my/id/eprint/9327
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