Title :

QUANTIFIED ASYMPTOTIC BEHAVIOUR OF BANACH SPACE OPERATORS AND APPLICATIONS TO ITERATIVE PROJECTION METHODS

Author(s) :

Badea, Catalin [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Seifert, David [Auteur]

Journal title :

Pure and Applied Functional Analysis

Publisher :

Yokohama Publishers

Publication date :

2017

ISSN :

2189-3756

English keyword(s) :

Rates of convergence
orbits
operators
Banach spaces
reflexivity
uniform convexity
uniform smoothness
numerical range
iterative projection methods

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

We present an extension of our earlier work [Ritt operators and convergence in the method of alternating projections, J. Approx. Theory, 205:133--148, 2016] by proving a general asymptotic result for orbits of an operator ...
Show more >We present an extension of our earlier work [Ritt operators and convergence in the method of alternating projections, J. Approx. Theory, 205:133--148, 2016] by proving a general asymptotic result for orbits of an operator acting on a reflexive Banach space. This result is obtained under a condition involving the growth of the resolvent, and we also discuss conditions involving the location and the geometry of the numerical range of the operator. We then apply the general results to some classes of iterative projection methods in approximation theory, such as the Douglas-Rachford splitting method and, under suitable geometric conditions either on the ambient Banach space or on the projection operators, the method of alternating projections.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL