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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, Volume 21, Number 3, Pages 546–555 (Mi vsgtu1548)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Modeling, Numerical Methods and Software Complexes

The row-oriented form of the regularized Kaczmarz's method

A. I. Zhdanov, Yu. V. Sidorov*

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: This paper presents the new iterative method for solving the standard Tikhonov regularization problem. The basis of the method is the application the projection Kaczmarz algorithm to the augmented regularized normal system of equations. The use of the augmented regularized normal system of equations, instead the system of regularized normal equations, makes it possible to significantly reduce the spectral condition number of the original problem. The paper presents the row-oriented form of the regularized Kaczmarz algorithm. This form of the regularized Kaczmarz algorithm allows to solve problems in which the data are received sequentially (line by line). The proposed algorithm makes it possible to effectively calculate solutions of problems with sparse matrices of large and superlarge dimensions. The comparison's results of the proposed row-oriented form of the algorithm with the column-oriented form of this algorithm are presented. By considering a certain classes of problems, the paper demonstrates that the proposed form of the regularized algorithm allows to reduce the number of iterations in comparison with the column-oriented form of the algorithm.

Keywords: iterative methods, projection algorithms, Tikhonov's regularization, Kaczmarz algorithm, row-oriented form of the regularized Kaczmarz's algorithm
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1548

Full text: PDF file (667 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 519.612
MSC: 65F10, 65F22
Received: June 7, 2017
Revised: August 22, 2017
Accepted: September 18, 2017
First online: November 9, 2017

Citation: A. I. Zhdanov, Yu. V. Sidorov, “The row-oriented form of the regularized Kaczmarz's method”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:3 (2017), 546–555

Citation in format AMSBIB
\Bibitem{ZhdSid17}
\by A.~I.~Zhdanov, Yu.~V.~Sidorov
\paper The row-oriented form of the regularized Kaczmarz's method
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 3
\pages 546--555
\mathnet{http://mi.mathnet.ru/vsgtu1548}
\crossref{https://doi.org/10.14498/vsgtu1548}
\zmath{https://zbmath.org/?q=an:06964803}
\elib{https://elibrary.ru/item.asp?id=32248396}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Y. V. Sidorov, “Single Acceleration Methods of the Kaczmarz Algorithm Regularized Modifications”, Procedia Computer Science, 154 (2018), 319–326  crossref  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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