TY - JOUR
T1 - Randomized Kaczmarz iteration methods
T2 - Algorithmic extensions and convergence theory
AU - Bai, Zhong Zhi
AU - Wu, Wen Ting
N1 - Publisher Copyright:
© 2023, The JJIAM Publishing Committee and Springer Nature Japan KK, part of Springer Nature.
PY - 2023/9
Y1 - 2023/9
N2 - We review and compare several representative and effective randomized projection iteration methods, including the randomized Kaczmarz method, the randomized coordinate descent method, and their modifications and extensions, for solving the large, sparse, consistent or inconsistent systems of linear equations. We also anatomize, extract, and purify the asymptotic convergence theories of these iteration methods, and discuss, analyze, and summarize their advantages and disadvantages from the viewpoints of both theory and computations.
AB - We review and compare several representative and effective randomized projection iteration methods, including the randomized Kaczmarz method, the randomized coordinate descent method, and their modifications and extensions, for solving the large, sparse, consistent or inconsistent systems of linear equations. We also anatomize, extract, and purify the asymptotic convergence theories of these iteration methods, and discuss, analyze, and summarize their advantages and disadvantages from the viewpoints of both theory and computations.
KW - Convergence property
KW - Coordinate descent method
KW - Kaczmarz method
KW - Randomized projection iteration
KW - System of linear equations
UR - https://www.scopus.com/pages/publications/85158122142
U2 - 10.1007/s13160-023-00586-7
DO - 10.1007/s13160-023-00586-7
M3 - Article
AN - SCOPUS:85158122142
SN - 0916-7005
VL - 40
SP - 1421
EP - 1443
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
IS - 3
ER -