NII Technical Report (NII-2020-003E)

Title Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems.
Authors Yi-shu Du, Ken Hayami, Ning Zheng, Keiichi Morikuni, Jun-Feng Yin
Abstract 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.
Language English
Published Jun 29, 2020
Pages 17p
PDF File 20-003E.pdf

NII Technical Reports
National Institute of Informatics