Numerical experiments with variations of the Gauss-Newton algorithm for nonlinear least squares |
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Authors: | E Spedicato M T Vespucci |
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Institution: | (1) Department of Mathematics, University of Bergamo, Bergamo, Italy |
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Abstract: | In this paper, the classical Gauss-Newton method for the unconstrained least squares problem is modified by introducing a quasi-Newton approximation to the second-order term of the Hessian. Various quasi-Newton formulas are considered, and numerical experiments show that most of them are more efficient on large residual problems than the Gauss-Newton method and a general purpose minimization algorithm based upon the BFGS formula. A particular quasi-Newton formula is shown numerically to be superior. Further improvements are obtained by using a line search that exploits the special form of the function. |
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Keywords: | Mathematical programming nonlinear programming nonlinear least squares quasi-Newton methods |
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