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An Evaluation of Mathematical Software that Solves Nonlinear Least Squares Problems

An Evaluation of Mathematical Software that Solves Nonlinear Least Squares Problems An Evaluation of Mathematical Software That Solves Nonlinear Least Squares Problems K. L. HIEBERT Sandla National Laboratories In this paper the "state of the art" of mathematical software that solves nonlinear least squares problems is evaluated. The evaluatmn is based on a comparison of 12 readily available FORTRAN codes. Theoretical and software aspects of the codes, as well as their performance on a carefully designed set of test problems, are used in the comparison. Key Words and Phrases: software evaluation, nonlinear least squares, nonlinear regression, nonlinear data fittmg, Levenberg-Marquardt, Gauss-Newton, augmented Gauss-Newton, quasi-Newton CR Categories: 4, 4.6, 5, 5.1 1. INTRODUCTION An integral part of the development of m a t h e m a t i c a l software is the testing of the software. One c o m m o n type of testing is comparison testing, t h a t is, comparing the performance of two or more codes t h a t claim to be able to solve the same type of problem, for the purpose of determining which code is "best." As a n y o n e who has ever been involved in testing software knows, testing to find a "best" http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

An Evaluation of Mathematical Software that Solves Nonlinear Least Squares Problems

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References (15)

Publisher
Association for Computing Machinery
Copyright
Copyright © 1981 by ACM Inc.
ISSN
0098-3500
DOI
10.1145/355934.355935
Publisher site
See Article on Publisher Site

Abstract

An Evaluation of Mathematical Software That Solves Nonlinear Least Squares Problems K. L. HIEBERT Sandla National Laboratories In this paper the "state of the art" of mathematical software that solves nonlinear least squares problems is evaluated. The evaluatmn is based on a comparison of 12 readily available FORTRAN codes. Theoretical and software aspects of the codes, as well as their performance on a carefully designed set of test problems, are used in the comparison. Key Words and Phrases: software evaluation, nonlinear least squares, nonlinear regression, nonlinear data fittmg, Levenberg-Marquardt, Gauss-Newton, augmented Gauss-Newton, quasi-Newton CR Categories: 4, 4.6, 5, 5.1 1. INTRODUCTION An integral part of the development of m a t h e m a t i c a l software is the testing of the software. One c o m m o n type of testing is comparison testing, t h a t is, comparing the performance of two or more codes t h a t claim to be able to solve the same type of problem, for the purpose of determining which code is "best." As a n y o n e who has ever been involved in testing software knows, testing to find a "best"

Journal

ACM Transactions on Mathematical Software (TOMS)Association for Computing Machinery

Published: Mar 1, 1981

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