The row-oriented form of the regularized Kaczmarz's method
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...
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Samara State Technical University
2017-11-01
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doaj-acab80bd29ca4be29f3cb6947c8ac4952020-11-25T00:35:42ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812017-11-0121354655510.14498/vsgtu1548The row-oriented form of the regularized Kaczmarz's method Alexander I. Zhdanov0Yury V. Sidorov1Samara State Technical University, Samara, 443100, Russian FederationSamara State Technical University, Samara, 443100, Russian FederationThis 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. http://mi.mathnet.ru/eng/vsgtu1548 iterative methodsprojection algorithmsTikhonov's regularizationKaczmarz algorithmrow-oriented form of the regularized Kaczmarz's algorithm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Alexander I. Zhdanov Yury V. Sidorov |
spellingShingle |
Alexander I. Zhdanov Yury V. Sidorov The row-oriented form of the regularized Kaczmarz's method Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki iterative methods projection algorithms Tikhonov's regularization Kaczmarz algorithm row-oriented form of the regularized Kaczmarz's algorithm |
author_facet |
Alexander I. Zhdanov Yury V. Sidorov |
author_sort |
Alexander I. Zhdanov |
title |
The row-oriented form of the regularized Kaczmarz's method |
title_short |
The row-oriented form of the regularized Kaczmarz's method |
title_full |
The row-oriented form of the regularized Kaczmarz's method |
title_fullStr |
The row-oriented form of the regularized Kaczmarz's method |
title_full_unstemmed |
The row-oriented form of the regularized Kaczmarz's method |
title_sort |
row-oriented form of the regularized kaczmarz's method |
publisher |
Samara State Technical University |
series |
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
issn |
1991-8615 2310-7081 |
publishDate |
2017-11-01 |
description |
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. |
topic |
iterative methods projection algorithms Tikhonov's regularization Kaczmarz algorithm row-oriented form of the regularized Kaczmarz's algorithm |
url |
http://mi.mathnet.ru/eng/vsgtu1548 |
work_keys_str_mv |
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