Variable projection for nonlinear least squares problems

Authors:
Dianne P. O'Leary;Bert W. Rust
Affiliations:
National Institute of Standards and Technology, Gaithersburg, USA and Computer Science Department and Institute for Advanced Computer Studies, University of Maryland, College Park, USA 20742;Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, USA 20899-8910
Venue:
Computational Optimization and Applications
Year:
2013

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Efficient implementation of a variable projection algorithm for nonlinear least squares problems

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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.