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Variable Projection for Nonlinear Least Squares Problems



Dianne M. O'Leary, Bert W. Rust


The variable projection algorithm of Golub and Pereyra (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 "modern" implementation of this algorithm so that it can be easily used. We consider how 35 years of changes in hardware and software influence our software design, and we provide a more robust algorithm that can also handle constraints on the parameters.
ACM Transactions on Mathematical Software


nonlinear least squares, variable projection algorithm, varpro


O'Leary, D. and Rust, B. (2012), Variable Projection for Nonlinear Least Squares Problems, ACM Transactions on Mathematical Software, [online], (Accessed April 24, 2024)
Created August 1, 2012, Updated October 12, 2021