On the solution of highly structured nonlinear equations
type: Item
instance of: scholarly article
title: On the solution of highly structured nonlinear equations
zbMATH Open document ID: 0755.65049
DOI: 10.1016/0377-0427(92)90184-Y
author: F. Soesianto
author: William E. Hart
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-16T00:00:00Z
review text: The authors discuss a quasi-Newton method which is able to take advantage of the sparsity properties of the Jacobian, \(A\), of a large nonlinear equation system. Their method directly updates each of the sparse \(L\) and \(U\) factors of \(B\), a linearization of \(A\), in contrast to the method of \textit{J. E. Dennis jun.} and \textit{E. S. Marwil} [Math. Comput. 38, 459-474 (1982; Zbl 0482.65028)] in which one of the factors is updated in a quasi-Newton manner, the other being held constant in a modified Newton fashion. The numerical solution of two-point boundary value problems by multiple shooting leads to the need to solve a sparse linear system. Several methods of solution of these linear equations, including the two above, are compared over five problems, one of which is a second order partial differential equation. The results of these and more extensive tests demonstrate the superlinear convergence of the new method (which is proved in the second author's doctoral thesis) and show that it is robust.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 89619
zbMATH Keywords: quasi-Newton method
zbMATH Keywords: large nonlinear equation system
zbMATH Keywords: two-point boundary value problems
zbMATH Keywords: multiple shooting
zbMATH Keywords: sparse linear system
zbMATH Keywords: superlinear convergence
reviewed by: Adrian Swift
describes a project that uses: PASVA3
MaRDI profile type: Publication
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full work available at URL: 0377-0427(92)90184-y
OpenAlex ID: W2000137406
description: scientific article; zbMATH DE number 89619