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A variable projection method for solving separable nonlinear least squares problems

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Abstract

Consider the separable nonlinear least squares problem of findinga εR n and α εR k which, for given data (y i ,t i ),i=1,2,...m, and functions ϕ j (α,t),j=1,2,...,n(m>n), minimize the functional

$$r(a,\alpha ) = \left\| {y - \Phi (\alpha )a} \right\|_2^2$$

where θ(α) ij =ϕ j (α,t i ). Golub and Pereyra have shown that this problem can be reduced to a nonlinear least squares problem involvingα only, and a linear least squares problem involvinga only. In this paper we propose a new method for determining the optimalα which computationally has proved more efficient than the Golub-Pereyra scheme.

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References

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Authors and Affiliations

  1. Computer Science Department, University of Aarhus, Aarhus, Denmark

    Linda Kaufman

  2. Computer Science Department, University of Colorado, 80302, Boulder, Colorado, USA

    Linda Kaufman

Authors
  1. Linda Kaufman
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Kaufman, L. A variable projection method for solving separable nonlinear least squares problems. BIT 15, 49–57 (1975). https://doi.org/10.1007/BF01932995

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  • DOI: https://doi.org/10.1007/BF01932995

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