A variable projection method for solving separable nonlinear least squares problems

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 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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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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Keywords

  • Computational Mathematic
  • Projection Method
  • Variable Projection
  • Variable Projection Method