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An Extension of the Gradient Algorithm

In: Numerical Optimization with Computational Errors

Author

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  • Alexander J. Zaslavski

    (The Technion – Israel Institute of Technology)

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.

Suggested Citation

  • Alexander J. Zaslavski, 2016. "An Extension of the Gradient Algorithm," Springer Optimization and Its Applications, in: Numerical Optimization with Computational Errors, chapter 0, pages 73-84, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-30921-7_5
    DOI: 10.1007/978-3-319-30921-7_5
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