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Volume 12, Issue 2
On Convergence of the Partially Randomized Extended Kaczmarz Method

Wen-Ting Wu

East Asian J. Appl. Math., 12 (2022), pp. 435-448.

Published online: 2022-02

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  • 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.

  • AMS Subject Headings

65F10, 65F20, 65K05, 90C25, 15A06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-435, author = {Wu , Wen-Ting}, title = {On Convergence of the Partially Randomized Extended Kaczmarz Method}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290921.240122}, url = {http://global-sci.org/intro/article_detail/eajam/20263.html} }
TY - JOUR T1 - On Convergence of the Partially Randomized Extended Kaczmarz Method AU - Wu , Wen-Ting JO - East Asian Journal on Applied Mathematics VL - 2 SP - 435 EP - 448 PY - 2022 DA - 2022/02 SN - 12 DO - http://doi.org/10.4208/eajam.290921.240122 UR - https://global-sci.org/intro/article_detail/eajam/20263.html KW - System of linear equations, Kaczmarz method, randomized iteration, convergence property. AB -

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.

Wen-Ting Wu. (2022). On Convergence of the Partially Randomized Extended Kaczmarz Method. East Asian Journal on Applied Mathematics. 12 (2). 435-448. doi:10.4208/eajam.290921.240122
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