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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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

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spelling	doaj-d62e8089b91744eb8d4f3df5e563efbc2021-03-09T02:14:26ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications 2146-09572146-57032019-04-019210.11121/ijocta.01.2019.00743A New Broyden rank reduction method to solve large systems of nonlinear equationsOuarit Mostafa0Ali Souissi1Mohamed Ziani2MACS Laboratory, Department of Mathematics and Computer Sciences, Faculty of Sciences Ain Chock, Hassan II University Of Casablanca, MoroccoNumerical Analysis Group, LMSA, CeReMAR, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, MoroccoNumerical Analysis Group. LMSA, CeReMAR, Department of Mathematics, Faculty of Sciences, Mohammed V University in RABAT 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. http://www.ijocta.org/index.php/files/article/view/743Large nonlinear systems of equationsLimited memory Broyden methodSingular values thresholdingRank reductionSuperlinear convergence.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ouarit Mostafa Ali Souissi Mohamed Ziani
spellingShingle	Ouarit Mostafa Ali Souissi Mohamed Ziani A New Broyden rank reduction method to solve large systems of nonlinear equations An International Journal of Optimization and Control: Theories & Applications Large nonlinear systems of equations Limited memory Broyden method Singular values thresholding Rank reduction Superlinear convergence.
author_facet	Ouarit Mostafa Ali Souissi Mohamed Ziani
author_sort	Ouarit Mostafa
title	A New Broyden rank reduction method to solve large systems of nonlinear equations
title_short	A New Broyden rank reduction method to solve large systems of nonlinear equations
title_full	A New Broyden rank reduction method to solve large systems of nonlinear equations
title_fullStr	A New Broyden rank reduction method to solve large systems of nonlinear equations
title_full_unstemmed	A New Broyden rank reduction method to solve large systems of nonlinear equations
title_sort	new broyden rank reduction method to solve large systems of nonlinear equations
publisher	Balikesir University
series	An International Journal of Optimization and Control: Theories & Applications
issn	2146-0957 2146-5703
publishDate	2019-04-01
description	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.
topic	Large nonlinear systems of equations Limited memory Broyden method Singular values thresholding Rank reduction Superlinear convergence.
url	http://www.ijocta.org/index.php/files/article/view/743
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A New Broyden rank reduction method to solve large systems of nonlinear equations

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