### Abstract

Original language | English |
---|---|

Pages (from-to) | 416-435 |

Number of pages | 20 |

Journal | SIAM Journal on Scientific and Statistical Computing |

Volume | 8 |

Issue number | 3 |

Publication status | Published - 1987 |

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*SIAM Journal on Scientific and Statistical Computing*, vol. 8, no. 3, pp. 416-435.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - On large scale nonlinear least squares calculations

AU - Toint, Philippe

PY - 1987

Y1 - 1987

N2 - 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.

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

SP - 416

EP - 435

JO - SIAM Journal on Scientific and Statistical Computing

JF - SIAM Journal on Scientific and Statistical Computing

SN - 0196-5204

IS - 3

ER -