On adaptive discretization schemes for the regularization of ill-posed problems with semiiterative methods

2014/07/19 by Wolfgang Erb, Erb, Wolfgang, Evgeniya V. Semenova +1
Computer Science · Mathematics · #47A52 #65F10 #65J20 #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1407.5189

openalex publication_date 2014/07/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a stopping criterion as the discrepancy principle or the balancing principle yields an order optimal regularization scheme and allows to reduce the computational costs.

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