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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR 2018: 0.881
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Online
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1569-3945
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Volume 23, Issue 6

Issues

Stochastic algorithms for solving linear and nonlinear inverse ill-posed problems for particle size retrieving and x-ray diffraction analysis of epitaxial films

Karl K. Sabelfeld
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  • Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, 630090, Novosibirsk, Lavrentieve Str. 6, Russia
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/ Nadezhda S. Mozartova
  • Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, 630090, Novosibirsk, Lavrentieve Str. 6, Russia
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Published Online: 2015-07-17 | DOI: https://doi.org/10.1515/jiip-2015-0043

Abstract

We suggest stochastic simulation techniques for solving two classes of linear and nonlinear inverse and ill-posed problems: (1) recovering the particle nanosize distribution from diffusion battery measurements, and (2) retrieving the step structure of the epitaxial films from the x-ray diffraction analysis. To solve these problems we develop three stochastic based methods: (1) the random projection method, a stochastic version of the Kaczmarz method, (2) a randomized SVD method, and (3) stochastic genetic algorithm. Results of comparative simulations of the three methods are also presented.

Keywords: Diffusion battery; particle size distribution; epitaxial films; x-ray diffraction; random projection method; Kaczmarz algorithm; randomized SVD; stochastic genetic algorithm

MSC: 65C05; 65C30; 35R30

About the article

Received: 2015-04-17

Revised: 2015-06-09

Accepted: 2015-06-16

Published Online: 2015-07-17

Published in Print: 2015-12-01


Funding Source: Russian Science Foundation

Award identifier / Grant number: 14-11-00083


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 6, Pages 673–686, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2015-0043.

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