Article ID: | iaor2013168 |
Volume: | 49 |
Issue: | 3 |
Start Page Number: | 365 |
End Page Number: | 379 |
Publication Date: | Mar 2011 |
Journal: | Journal of Global Optimization |
Authors: | Yassine Adnan, Benahmed Boubakeur, Mokhtar-Kharroubi Hocine, Malafosse Bruno |
Keywords: | quasi-Newton method, Hilbert space |
In the first part of this paper, we give a survey on convergence rates analysis of quasi‐Newton methods in infinite Hilbert spaces for nonlinear equations. Then, in the second part we apply quasi‐Newton methods in their Hilbert formulation to solve matrix equations. So, we prove, under natural assumptions, that quasi‐Newton methods converge locally and superlinearly; the global convergence is also studied. For numerical calculations, we propose new formulations of these methods based on the matrix representation of the dyadic operator and the vectorization of matrices. Finally, we apply our results to algebraic Riccati equations.