| Title:
|
A hybrid method for nonlinear least squares that uses quasi-Newton updates applied to an approximation of the Jacobian matrix (English) |
| Author:
|
Lukšan, Ladislav |
| Author:
|
Vlček, Jan |
| Language:
|
English |
| Journal:
|
Programs and Algorithms of Numerical Mathematics |
| Volume:
|
Proceedings of Seminar. Hejnice, June 24-29, 2018 |
| Issue:
|
2018 |
| Year:
|
|
| Pages:
|
99-106 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\|A d + f\|$ 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. (English) |
| Keyword:
|
nonlinear least squares |
| Keyword:
|
hybrid methods |
| Keyword:
|
trust-region methods |
| Keyword:
|
quasi-Newton methods |
| Keyword:
|
numerical algorithms |
| Keyword:
|
numerical experiments |
| MSC:
|
65F30 |
| MSC:
|
65K10 |
| DOI:
|
10.21136/panm.2018.11 |
| . |
| Date available:
|
2019-04-29T13:37:03Z |
| Last updated:
|
2023-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703066 |
| . |
