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Variable projection for nonlinear least squares problems

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  • Dianne O’Leary
  • Bert Rust

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. Copyright US National Institute of Standards and Technology 2013

Suggested Citation

  • Dianne O’Leary & Bert Rust, 2013. "Variable projection for nonlinear least squares problems," Computational Optimization and Applications, Springer, vol. 54(3), pages 579-593, April.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:3:p:579-593
    DOI: 10.1007/s10589-012-9492-9
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    References listed on IDEAS

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    1. Mullen, Katharine M. & van Stokkum, Ivo H. M., 2007. "TIMP: An R Package for Modeling Multi-way Spectroscopic Measurements," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 18(i03).
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    Cited by:

    1. Stolbunov, Valentin & Nair, Prasanth B., 2018. "Sparse radial basis function approximation with spatially variable shape parameters," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 170-184.
    2. Kovács, Péter & Fekete, Andrea M., 2019. "Nonlinear least-squares spline fitting with variable knots," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 490-501.
    3. Maximilian S. Ernst & Aaron Peikert & Andreas M. Brandmaier & Yves Rosseel, 2023. "A Note on the Connection Between Trek Rules and Separable Nonlinear Least Squares in Linear Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 98-116, March.
    4. Adelina Bärligea & Philipp Hochstaffl & Franz Schreier, 2023. "A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing," Mathematics, MDPI, vol. 11(13), pages 1-20, June.
    5. Zheng, Sanpeng & Feng, Renzhong, 2023. "A variable projection method for the general radial basis function neural network," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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