Error bounds for the method of simultaneous projections with infinitely many subspaces

JOURNAL OF APPROXIMATION THEORY

卷:272

Article

Reich, Simeon¹  Zalas, Rafal¹ 

[1] Technion Israel Inst Technol, Dept Math, IL-3200003 Haifa, Israel

关键词: Friedrichs angle;    Product space;    Rates of convergence;    Simultaneous projection method;   

DOI  :  10.1016/j.jat.2021.105648

来源: Elsevier

【 摘 要 】

We investigate the properties of the simultaneous projection method as applied to countably infinitely many closed and linear subspaces of a real Hilbert space. We establish the optimal error bound for linear convergence of this method, which we express in terms of the cosine of the Friedrichs angle computed in an infinite product space. In addition, we provide estimates and alternative expressions for the above-mentioned number. Furthermore, we relate this number to the dichotomy theorem and to super-polynomially fast convergence. We also discuss polynomial convergence of the simultaneous projection method which takes place for particularly chosen starting points. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free