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

An International Journal of Optimization and Control: Theories & Applications

article

Ouarit Mostafa¹  Ali Souissi²  Mohamed Ziani³ 

[1] MACS Laboratory, Department of Mathematics and Computer Sciences,Faculty of Sciences Ain Chock, Hassan II University Of Casablanca;Numerical Analysis Group, LMSA, CeReMAR, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat;Numerical Analysis Group. LMSA, CeReMAR,Department of Mathematics,Faculty of Sciences,Mohammed V University in RABAT

关键词: Large nonlinear systems of equations;    Limited memory Broyden method;    Singular values thresholding;    Rank reduction;    Superlinear convergence.;   

DOI  :  10.11121/ijocta.01.2019.00743

学科分类：地球科学(综合)

来源: Balikesir University

【 摘 要 】

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.

【 授权许可】

CC BY