eng
Lukšan, Ladislav
Vlček, Jan
A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix
nonlinear least squares
hybrid methods
trust-region methods
quasi-Newton methods
numerical algorithms
numerical experiments
http://hdl.handle.net/11104/0289769
http://www.nusl.cz/ntk/nusl-391451
In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that AT f = JT f. This property allows us to solve a linear least squares problem, minimizing ∥Ad+f∥ instead of solving the normal equation ATAd+JT f = 0, where d ∈ Rn is the required direction vector. Computational experiments confirm the efficiency of the new method.
2019