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Research Article | Open Access

A two-step randomized Gauss-Seidel method for solving large-scale linear least squares problems

Yimou Liao1, Tianxiu Lu1,2( ), Feng Yin1
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Bridge Non-destruction Detecting and Engineering Computing Key Laboratory, Zigong 643000, China
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Abstract

A two-step randomized Gauss-Seidel (TRGS) method is presented for large linear least squares problem with tall and narrow coefficient matrix. The TRGS method projects the approximate solution onto the solution space by given two random columns and is proved to be convergent when the coefficient matrix is of full rank. Several numerical examples show the effectiveness of the TRGS method among all methods compared.

Keywords

linear least-squares problemtwo-step iterative methodconvergence propertyGauss-Seidel

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Electronic Research Archive
Volume 30 Issue 2,
February 2022
Pages 755-779
DOI: 10.3934/era.2022040

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Cite this article:
Liao Y, Lu T, Yin F. A two-step randomized Gauss-Seidel method for solving large-scale linear least squares problems. Electronic Research Archive, 2022, 30(2): 755-779. https://doi.org/10.3934/era.2022040

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Received: 20 December 2021
Revised: 11 February 2022
Accepted: 20 February 2022
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)