Year: 2022
Author: Wen-Ting Wu
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 435–448
Abstract
To complete the convergence theory of the partially randomized extended Kaczmarz method for solving large inconsistent systems of linear equations, we give its convergence theorem whether the coefficient matrix is of full rank or not, tall or flat. This convergence theorem also modifies the existing upper bound for the expected solution error of the partially randomized extended Kaczmarz method when the coefficient matrix is tall and of full column rank. Numerical experiments show that the partially randomized extended Kaczmarz method is convergent when the tall or flat coefficient matrix is rank deficient, and can also converge faster than the randomized extended Kaczmarz method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.290921.240122
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 435–448
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: System of linear equations Kaczmarz method randomized iteration convergence property.