### 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 language | English |
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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 |