A New Broyden rank reduction method to solve large systems of nonlinear equations

A New Broyden rank reduction method to solve large systems of nonlinear equations

We propose a modification of limited memory Broyden methods, called dynamical Broyden rank reduction method, to solve high dimensional systems of nonlinear equations. Based on a thresholding process of singular values, the proposed method determines a priori the rank of the reduced update matrix. I...

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Bibliographic Details
Main Authors: Ouarit Mostafa, Ali Souissi, Mohamed Ziani
Format: Article
Language:English
Published: Balikesir University 2019-04-01
Series:An International Journal of Optimization and Control: Theories & Applications
Subjects:
Large nonlinear systems of equations
Limited memory Broyden method
Singular values thresholding
Rank reduction
Superlinear convergence.
Online Access:http://www.ijocta.org/index.php/files/article/view/743
Description
Summary:We propose a modification of limited memory Broyden methods, called dynamical Broyden rank reduction method, to solve high dimensional systems of nonlinear equations. Based on a thresholding process of singular values, the proposed method determines a priori the rank of the reduced update matrix. It significantly reduces the number of singular values decomposition calls of the update matrix during the iterations. Local superlinear convergence of the method is proved and some numerical examples are displayed.
ISSN:2146-0957
2146-5703

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