On the finitary content of Dykstra’s cyclic projections algorithm

  • Pedro Pinto

    Technische Universität Darmstadt, Darmstadt, Germany
On the finitary content of Dykstra’s cyclic  projections algorithm cover

A subscription is required to access this article.

Abstract

We study the asymptotic behaviour of the well-known Dykstra’s algorithm. We provide an elementary proof for the convergence of Dykstra’s algorithm in which the standard argument is stripped to its central features and where the original compactness principles are circumvented, additionally providing highly uniform computable rates of metastability in a fully general setting. Moreover, under an additional assumption, we are even able to obtain effective general rates of convergence. We argue that such an additional condition is actually necessary for the existence of general uniform rates of convergence.

Cite this article

Pedro Pinto, On the finitary content of Dykstra’s cyclic projections algorithm. Z. Anal. Anwend. (2024), published online first

DOI 10.4171/ZAA/1768