| Full text | |
| Author(s): |
Goncalves, Douglas S.
;
Santos, Sandra A.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | NUMERICAL ALGORITHMS; v. 73, n. 2, p. 407-431, OCT 2016. |
| Web of Science Citations: | 4 |
| Abstract | |
A simple spectral correction for the Gauss-Newton model applied to nonlinear least squares problems is presented. Such a correction consists in adding a sign-free multiple of the identity to the Hessian of the Gauss-Newton model, being the multiple based on spectral approximations for the Hessians of the residual functions. A detailed local convergence analysis is provided for the resulting method applied to the class of quadratic residual problems. Under mild assumptions, the proposed method is proved to be convergent for problems for which the convergence of the Gauss-Newton method might not be ensured. Moreover, the rate of linear convergence is proved to be better than the Gauss-Newton's one for a class of non-zero residue problems. These theoretical results are illustrated by numerical examples with quadratic and non-quadratic residual problems. (AU) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 13/05475-7 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |