Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations |
| |
Authors: | Boubakeur Benahmed Hocine Mokhtar-Kharroubi Bruno de Malafosse Adnan Yassine |
| |
Affiliation: | 1.Département de Mathématiques et Informatique,ENSET d’Oran,El m’naouer,Algérie;2.Département de Mathématiques, Faculté des sciences,Université d’Oran,El m’naouer,Algérie;3.Laboratoire de Mathématiques Appliquées du Havre,Université du Havre,Le Havre Cedex,France |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|