@inproceedings{b9524db1427e4a2abed21ba4d1a5ecb8,
title = "Remarks on kaczmarz algorithm for solving consistent and inconsistent system of linear equations",
abstract = "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.",
keywords = "Convergence rate, Iterative methods, Kaczmarz method, Linear systems, Orthogonal projection",
author = "Xinyin Huang and Gang Liu and Qiang Niu",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.; 20th International Conference on Computational Science, ICCS 2020 ; Conference date: 03-06-2020 Through 05-06-2020",
year = "2020",
doi = "10.1007/978-3-030-50417-5_17",
language = "English",
isbn = "9783030504168",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "225--236",
editor = "Krzhizhanovskaya, {Valeria V.} and G{\'a}bor Z{\'a}vodszky and Lees, {Michael H.} and Sloot, {Peter M.A.} and Sloot, {Peter M.A.} and Sloot, {Peter M.A.} and Dongarra, {Jack J.} and S{\'e}rgio Brissos and Jo{\~a}o Teixeira",
booktitle = "Computational Science – ICCS 2020 - 20th International Conference, Proceedings",
}