||Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems.
||Yi-shu Du, Ken Hayami, Ning Zheng, Keiichi Morikuni, Jun-Feng Yin
||We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners
for the right-preconditioned flexible GMRES method to solve consistent linear systems, with
a parameter tuning strategy for adjusting the number of inner iterations and the relaxation parameter.
We also present theoretical justifications of the right-preconditioned flexible GMRES for
solving consistent linear systems. Numerical experiments on overdetermined and underdetermined
linear systems show that the proposed method is superior to the GMRES method preconditioned by
NE-SOR inner iterations in terms of total CPU time.
||Jun 29, 2020