An Extension of the Gradient Algorithm

Alexander J. Zaslavski
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Alexander J. Zaslavski: The Technion – Israel Institute of Technology

Chapter Chapter 5 in Numerical Optimization with Computational Errors, 2016, pp 73-84 from Springer

Abstract: Abstract In this chapter we analyze the convergence of a gradient type algorithm, under the presence of computational errors, which was introduced by Beck and Teboulle [20] for solving linear inverse problems arising in signal/image processing. We show that the algorithm generates a good approximate solution, if computational errors are bounded from above by a small positive 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.

Keywords: Gradient-type Algorithms; Teboulle; Computational Errors; Small Positive Constant; Good Approximate Solution (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-30921-7_5

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DOI: 10.1007/978-3-319-30921-7_5

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