The alternating algorithm in a uniformly convex and uniformly smooth Banach space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:421

Article

Pinkus, Allan

关键词: Alternating algorithm;    Uniformly convex;    Uniformly smooth;   

DOI  :  10.1016/j.jmaa.2014.06.076

来源: Elsevier

【 摘 要 】

Let X be a uniformly convex and uniformly smooth Banach space. Assume that the M-i, i = 1,..., r, are closed linear subspaces of X, P-Mi is the best approximation operator to the linear subspace M-i and M := M-1 +...+ M-r. We prove that if M is closed, then the alternating algorithm given by repeated iterations of (I - P-Mr) (I - PMr-1) ... (I - P-M1) applied to any x is an element of X converges to x - P(M)x is the best approximation Operator to the linear subspace M. This result, in the case r = 2, was proven in Deutsch [4]. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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