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Numerical experiments with variations of the Gauss-Newton algorithm for nonlinear least squares

  • E. Spedicato
  • M. T. Vespucci
Contributed Papers

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.

Key Words

Mathematical programming nonlinear programming nonlinear least squares quasi-Newton methods 

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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • E. Spedicato
    • 1
  • M. T. Vespucci
    • 1
  1. 1.Department of MathematicsUniversity of BergamoBergamoItaly

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