An efficient variable projection formulation for separable nonlinear least squares problems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Article number6553163
Pages (from-to)707-711
Journal / PublicationIEEE Transactions on Cybernetics
Issue number5
Online published3 Jul 2013
Publication statusPublished - May 2014


We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time. © 2013 IEEE.

Research Area(s)

  • Matrix decomposition, parameter estimation, separable nonlinear least squares problems, variable projection