Computational Optimization and Applications

, Volume 54, Issue 3, pp 579–593 | Cite as

Variable projection for nonlinear least squares problems

Article

Abstract

The variable projection algorithm of Golub and Pereyra (SIAM J. Numer. Anal. 10:413–432, 1973) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a better likelihood of finding a global minimizer rather than a local one. The purpose of our work is to provide a more robust implementation of this algorithm, include constraints on the parameters, more clearly identify key ingredients so that improvements can be made, compute the Jacobian matrix more accurately, and make future implementations in other languages easy.

Keywords

Data fitting Model fitting Variable projection method Nonlinear least squares problems Jacobian approximation Least squares approximation Statistical software Mathematical software design and analysis 

Notes

Acknowledgements

We are grateful to Ronald F. Boisvert, Julianne Chung, David E. Gilsinn, Katharine M. Mullen, and the referee for helpful comments on the manuscript.

Supplementary material

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Copyright information

© US National Institute of Standards and Technology 2012

Authors and Affiliations

  1. 1.National Institute of Standards and TechnologyGaithersburgUSA
  2. 2.Computer Science Department and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA
  3. 3.Applied and Computational Mathematics DivisionNational Institute of Standards and TechnologyGaithersburgUSA

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