Inexact overlapped block Broyden methods for solving nonlinear equations
type: Item
instance of: scholarly article
title: Inexact overlapped block Broyden methods for solving nonlinear equations
zbMATH Open document ID: 1030.65048
DOI: 10.1016/S0096-3003(02)00026-7
author: Yurong Chen
author: Dayong Cai
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The paper is concerned with the problem of solving a large system of nonlinear equations. Many methods are suitable for this: Newton methods, inexact Newton methods, nonlinear block-iterative methods, inexact Newton-Krylov methods, etc. The authors discuss the inexact Broyden method with partially overlap which is a generalization of the parallelizable Jacobi-type block Broyden method. By directly performing the block Broyden iteration for the overlapped blocks and by assembling the overlapping parts of the results into an average weighted manner at each iteration, the block Broyden method is accelerated. A new algorithm which is a generalization of the block Broyden method with partially overlapped blocks is presented and the local convergence of this algorithm is proved. The implementation of the algorithm by several strategies for partitioning the Jacobian into weakly coupled partially ovelapped blocks is discussed and one numerical example (a system of \(N\) nonlinear equations) is performed by ten variants of the iterations.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 1861383
zbMATH Keywords: nonlinear equations
zbMATH Keywords: block-iterative solution
zbMATH Keywords: Broyden methods
zbMATH Keywords: graph partitioning
zbMATH Keywords: parallel computation
zbMATH Keywords: large system
zbMATH Keywords: algorithm
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
reviewed by: Iulian Coroian
describes a project that uses: KELLEY
describes a project that uses: Chaco
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1861383