Algorithms for the Solution of the Nonlinear Least-Squares Problem

This paper describes a modification to the Gauss-Newton method for the solution of nonlinear least-squares problems. The new method seeks to avoid the deficiencies in the Gauss-Newton method by improving, when necessary, the Hessian approximation by specifically including or approximating some of th...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 15; no. 5; pp. 977 - 992
Main Authors Gill, Philip E., Murray, Walter
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.10.1978
Subjects
Algorithms
Approximation
Curvature
Factorization
Hessian matrices
Laboratories
Least squares
Local minimum
Mathematical functions
Matrices
Scalars
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ISSN0036-1429
1095-7170
DOI10.1137/0715063

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Summary:This paper describes a modification to the Gauss-Newton method for the solution of nonlinear least-squares problems. The new method seeks to avoid the deficiencies in the Gauss-Newton method by improving, when necessary, the Hessian approximation by specifically including or approximating some of the neglected terms. The method seeks to compute the search direction without the need to form explicitly either the Hessian approximation or a factorization of this matrix. The benefits of this are similar to that of avoiding the formation of the normal equations in the Gauss-Newton method. Three algorithms based on this method are described: one which assumes that second derivative information is available and two which only assume first derivatives can be computed.
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ISSN:0036-1429
1095-7170
DOI:10.1137/0715063