Home > Conference materials > Papers > A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix

Original title:
A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix
Authors:
Lukšan, Ladislav ; Vlček, Jan Document type: Papers Conference/Event: Programs and Algorithms of Numerical Mathematics /19./, Hejnice (CZ), 20180624
Year:
2019
Language:
eng Abstract:
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.
Keywords:
hybrid methods; nonlinear least squares; numerical algorithms; numerical experiments; quasi-Newton methods; trust-region methods Host item entry: Programs and Algorithms of Numerical Mathematics 19, ISBN 978-80-85823-69-1

Institution: Institute of Computer Science AS ČR
(web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences. Original record: http://hdl.handle.net/11104/0289769