ALGORITHM 768 - TENSOLVE - A SOFTWARE PACKAGE FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS AND NONLINEAR LEAST-SQUARES PROBLEMS USING TENSOR METHODS

Citation
A. Bouaricha et Rb. Schnabel, ALGORITHM 768 - TENSOLVE - A SOFTWARE PACKAGE FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS AND NONLINEAR LEAST-SQUARES PROBLEMS USING TENSOR METHODS, ACM transactions on mathematical software, 23(2), 1997, pp. 174-195
Citations number
11
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Sciences",Mathematics,"Computer Science Software Graphycs Programming",Mathematics
ISSN journal
0098-3500
Volume
23
Issue
2
Year of publication
1997
Pages
174 - 195
Database
ISI
SICI code
0098-3500(1997)23:2<174:A7-T-A>2.0.ZU;2-#
Abstract
This article describes a modular software package for solving systems of nonlinear equations and nonlinear least-squares problems, using a n ew class of methods called tensor methods. It is intended for small-to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or to ap proximate it by finite differences at each iteration. The software all ows the user to choose between a tensor method and a standard method b ased on a linear model. The tensor method approximates F(x) by a quadr atic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard line ar model. Moreover, the software provides two different global strateg ies: a line search approach and a two-dimensional trust region approac h. Test results indicate that, in general, tensor methods are signific antly more efficient and robust than standard methods on small-and med ium-sized problems in iterations and function evaluations.