Convergence rate results for steepest descent type method for nonlinear ill-posed equations

Santhosh George and M. Sabari

Applied Mathematics and Computation, 2017, vol. 294, issue C, 169-179

Abstract: Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper.

Keywords: Nonlinear ill-posed problem; Steepest descent method; Minimal error method; Regularization method; Discrepancy principle (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:294:y:2017:i:c:p:169-179

DOI: 10.1016/j.amc.2016.09.009

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