Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods

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 i...

詳細記述

書誌詳細
主要な著者: Badea, C, Seifert, D
フォーマット: Journal article
出版事項: Yokohama Publishers 2017
その他の書誌記述
要約: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.