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Publication Date:
November 2008
ISSN:
1569-3945
DOI:
10.1515/JIIP.2008.041

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Journal of Inverse and III-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Relative computational efficiency of iteratively regularized methods

A. B. Bakushinsky1 / A. Smirnova2 / N. Tuncer3

1Institute of System Analysis Russian Academy of Sciences, 117312 Moscow, Russia. Email: bakush@isa.ru

2Dept. of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA. Email: asmirnova@gsu.edu

3Dept. of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA. Email: ntuncer@gsu.edu

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 7, Pages 681–694, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.041, November 2008

Publication History:
Received:
2008-02-28
Revised:
2008-03-05
Published Online:
2008-11-21

Abstract

The estimates for the number of operations needed to implement two different iteratively regularized Gauss–Newton methods as well as the iteratively regularized gradient scheme are given. The operation count is illustrated by simulations for a two dimensional version of the exponentially ill-posed optical tomography inverse problem for the diffusion (D) and absorption (μa) coefficient spatial distributions.

Key words.: Regularization; Fréchet and Gâteaux derivatives; Gauss–Newton method; optical tomography

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