A hybrid method for nonlinear least squares that uses quasi-Newton updates applied to an approximation of the Jacobian matrix

Lukšan, Ladislav, and Vlček, Jan. "A hybrid method for nonlinear least squares that uses quasi-Newton updates applied to an approximation of the Jacobian matrix." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2019. 99-106. <http://eudml.org/doc/294939>.

@inProceedings{Lukšan2019,
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 $A^T f = J^T f$. This property allows us to solve a linear least squares problem, minimizing $\Vert A d + f\Vert $ instead of solving the normal equation $A^T A d + J^T f = 0$, where $d \in R^n$ is the required direction vector. Computational experiments confirm the efficiency of the new method.},
author = {Lukšan, Ladislav, Vlček, Jan},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments},
location = {Prague},
pages = {99-106},
publisher = {Institute of Mathematics CAS},
title = {A hybrid method for nonlinear least squares that uses quasi-Newton updates applied to an approximation of the Jacobian matrix},
url = {http://eudml.org/doc/294939},
year = {2019},
}

TY - CLSWK
AU - Lukšan, Ladislav
AU - Vlček, Jan
TI - A hybrid method for nonlinear least squares that uses quasi-Newton updates applied to an approximation of the Jacobian matrix
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2019
CY - Prague
PB - Institute of Mathematics CAS
SP - 99
EP - 106
AB - 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 $A^T f = J^T f$. This property allows us to solve a linear least squares problem, minimizing $\Vert A d + f\Vert $ instead of solving the normal equation $A^T A d + J^T f = 0$, where $d \in R^n$ is the required direction vector. Computational experiments confirm the efficiency of the new method.
KW - nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments
UR - http://eudml.org/doc/294939
ER -