Methods with Remotest Set Control in a Hilbert Space

Alexander J. Zaslavski
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Alexander J. Zaslavski: Technion, Israel Institute of Technology

Chapter Chapter 5 in Solutions of Fixed Point Problems with Computational Errors, 2024, pp 213-250 from Springer

Abstract: Abstract In this chapter we study the convergence of methods with remotest set control 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 iterative method 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.

Date: 2024
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DOI: 10.1007/978-3-031-50879-0_5

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