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 - <p style="text-align: justify;">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.</p>