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The Cimmino Algorithm in a Hilbert Space

In: Solutions of Fixed Point Problems with Computational Errors

Author

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  • Alexander J. Zaslavski

    (Technion, Israel Institute of Technology)

Abstract

In this chapter we study the convergence of the Cimmino algorithm for solving star-shaped feasibility problems in a Hilbert space. Our main goal is to obtain an approximate solution of the problem in the presence of computational errors. We show that the Cimmino algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.

Suggested Citation

  • Alexander J. Zaslavski, 2024. "The Cimmino Algorithm in a Hilbert Space," Springer Optimization and Its Applications, in: Solutions of Fixed Point Problems with Computational Errors, chapter 0, pages 85-136, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-50879-0_3
    DOI: 10.1007/978-3-031-50879-0_3
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