Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations

In this paper we consider the classical Kaczmarz algorithm for solving system of linear equations. Based on the geometric relationship between the error vector and rows of the coefficient matrix, we derive the optimal strategy of selecting rows at each step of the algorithm for solving consistent sy...

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Detalles Bibliográficos
Autores principales: Huang, Xinyin, Liu, Gang, Niu, Qiang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7302833/
http://dx.doi.org/10.1007/978-3-030-50417-5_17
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author Huang, Xinyin
Liu, Gang
Niu, Qiang
author_facet Huang, Xinyin
Liu, Gang
Niu, Qiang
author_sort Huang, Xinyin
collection PubMed
description In this paper we consider the classical Kaczmarz algorithm for solving system of linear equations. Based on the geometric relationship between the error vector and rows of the coefficient matrix, we derive the optimal strategy of selecting rows at each step of the algorithm for solving consistent system of linear equations. For solving perturbed system of linear equations, a new upper bound in the convergence rate of the randomized Kaczmarz algorithm is obtained.
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spelling pubmed-73028332020-06-19 Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations Huang, Xinyin Liu, Gang Niu, Qiang Computational Science – ICCS 2020 Article In this paper we consider the classical Kaczmarz algorithm for solving system of linear equations. Based on the geometric relationship between the error vector and rows of the coefficient matrix, we derive the optimal strategy of selecting rows at each step of the algorithm for solving consistent system of linear equations. For solving perturbed system of linear equations, a new upper bound in the convergence rate of the randomized Kaczmarz algorithm is obtained. 2020-06-15 /pmc/articles/PMC7302833/ http://dx.doi.org/10.1007/978-3-030-50417-5_17 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Huang, Xinyin
Liu, Gang
Niu, Qiang
Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations
title Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations
title_full Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations
title_fullStr Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations
title_full_unstemmed Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations
title_short Remarks on Kaczmarz Algorithm for Solving Consistent and Inconsistent System of Linear Equations
title_sort remarks on kaczmarz algorithm for solving consistent and inconsistent system of linear equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7302833/
http://dx.doi.org/10.1007/978-3-030-50417-5_17
work_keys_str_mv AT huangxinyin remarksonkaczmarzalgorithmforsolvingconsistentandinconsistentsystemoflinearequations
AT liugang remarksonkaczmarzalgorithmforsolvingconsistentandinconsistentsystemoflinearequations
AT niuqiang remarksonkaczmarzalgorithmforsolvingconsistentandinconsistentsystemoflinearequations

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