Open AccessA two-step randomized Gauss-Seidel method for solving large-scale linear least squares problems
Author(s) -
Yimou Liao,
Tianxiu Lu,
Feng Yin
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022040
Subject(s) - gauss–seidel method , mathematics , coefficient matrix , rank (graph theory) , matrix (chemical analysis) , linear least squares , least squares function approximation , scale (ratio) , mathematical optimization , iterative method , statistics , combinatorics , linear model , chemistry , chromatography , physics , eigenvalues and eigenvectors , quantum mechanics , estimator
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.