On large scale nonlinear least squares calculations

Research output: Contribution to journalArticle

Abstract

The nonlinear model fitting problem is analyzed in this paper, with special emphasis on the practical solution techniques when the number of parameters in the model is large. Classical approaches to small dimensional least squares are reviewed and an extension of them to problems involving many variables is proposed. This extension uses the concept of partially separable structures, which has already proved its applicability for large scale optimization. An adaptable algorithm is discussed, which chooses between various possible models of the objective function. Preliminary numerical experience is also presented, which shows that actual solution of a large class of fitting problems involving several hundreds of nonlinear parameters is possible at a reasonable cost.
Original languageEnglish
Pages (from-to)416-435
Number of pages20
JournalSIAM Journal on Scientific and Statistical Computing
Volume8
Issue number3
Publication statusPublished - 1987

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title = "On large scale nonlinear least squares calculations",
abstract = "The nonlinear model fitting problem is analyzed in this paper, with special emphasis on the practical solution techniques when the number of parameters in the model is large. Classical approaches to small dimensional least squares are reviewed and an extension of them to problems involving many variables is proposed. This extension uses the concept of partially separable structures, which has already proved its applicability for large scale optimization. An adaptable algorithm is discussed, which chooses between various possible models of the objective function. Preliminary numerical experience is also presented, which shows that actual solution of a large class of fitting problems involving several hundreds of nonlinear parameters is possible at a reasonable cost.",
author = "Philippe Toint",
year = "1987",
language = "English",
volume = "8",
pages = "416--435",
journal = "SIAM Journal on Scientific and Statistical Computing",
issn = "0196-5204",
number = "3",

}

On large scale nonlinear least squares calculations. / Toint, Philippe.

In: SIAM Journal on Scientific and Statistical Computing, Vol. 8, No. 3, 1987, p. 416-435.

Research output: Contribution to journalArticle

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T1 - On large scale nonlinear least squares calculations

AU - Toint, Philippe

PY - 1987

Y1 - 1987

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AB - The nonlinear model fitting problem is analyzed in this paper, with special emphasis on the practical solution techniques when the number of parameters in the model is large. Classical approaches to small dimensional least squares are reviewed and an extension of them to problems involving many variables is proposed. This extension uses the concept of partially separable structures, which has already proved its applicability for large scale optimization. An adaptable algorithm is discussed, which chooses between various possible models of the objective function. Preliminary numerical experience is also presented, which shows that actual solution of a large class of fitting problems involving several hundreds of nonlinear parameters is possible at a reasonable cost.

M3 - Article

VL - 8

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EP - 435

JO - SIAM Journal on Scientific and Statistical Computing

JF - SIAM Journal on Scientific and Statistical Computing

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