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The method of cyclic projections for closed convex sets in a Hilbert space under the presence of computational errors

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Abstract

In this paper, we study the method of cyclic projections for inconsistent convex feasibility problems in a Hilbert space under the presence of computational errors. We show that our algorithm generates a good approximate solution, if computational errors are bounded from above by a small positive constant. Our main goal is, for a known computational error, to find out what approximate solution can be obtained and how many iterates one needs for this.

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Acknowledgements

The author thanks anonymous referees for careful reading the paper and providing him with useful comments.

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Authors and Affiliations

  1. Department of Mathematics, The Technion Israel Institute of Technology, 32000, Haifa, Israel

    Alexander J. Zaslavski

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  1. Alexander J. Zaslavski
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Correspondence to Alexander J. Zaslavski.

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Zaslavski, A.J. The method of cyclic projections for closed convex sets in a Hilbert space under the presence of computational errors. Numer Algor 91, 1427–1439 (2022). https://doi.org/10.1007/s11075-022-01308-9

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