Authors

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

Journal title

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.