Remarks on kaczmarz algorithm for solving consistent and inconsistent system of linear equations

Xinyin Huang, Gang Liu*, Qiang Niu

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingConference Proceedingpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationComputational Science – ICCS 2020 - 20th International Conference, Proceedings
EditorsValeria V. Krzhizhanovskaya, Gábor Závodszky, Michael H. Lees, Peter M.A. Sloot, Peter M.A. Sloot, Peter M.A. Sloot, Jack J. Dongarra, Sérgio Brissos, João Teixeira
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783030504168
Publication statusPublished - 2020
Event20th International Conference on Computational Science, ICCS 2020 - Amsterdam, Netherlands
Duration: 3 Jun 20205 Jun 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12138 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th International Conference on Computational Science, ICCS 2020


  • Convergence rate
  • Iterative methods
  • Kaczmarz method
  • Linear systems
  • Orthogonal projection

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