TY - JOUR
T1 - Faster Deterministic Pseudoinverse-Free Block Extension of Motzkin Method for Large Consistent Linear Systems
AU - Zhao , Jing
AU - Zhang , Jianhua
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 914
EP - 934
PY - 2023
DA - 2023/10
SN - 13
DO - http://doi.org/10.4208/eajam.2022-203.140123
UR - https://global-sci.org/intro/article_detail/eajam/22068.html
KW - Block Kaczmarz method, consistent linear system, maximum residual, heavy ball momentum.
AB - <p style="text-align: justify;">Recently, a fast deterministic block Kaczmarz (FDBK) method which uses
a greedy criterion of the row selections and contains pseudoinverse-free computation
is presented. In this work, we introduce a maximum residual rule into FDBK and develop a new block Kaczmarz method which is also considered as a fast deterministic
pseudoinverse-free block extension of Motzkin (FBEM) method. In addition, we prove
that FBEM converges linearly to the unique least-norm solution of the linear systems.
Furthermore, by incorporating the Polyak momentum technique into the FBEM iteration
method, we establish an accelerated variant of FBEM (mFBEM) and show its global linear convergence. Numerical examples using artificial and real datasets demonstrate the
effectiveness of FBEM as well as mFBEM.</p>