TY - JOUR
T1 - An Efficient Variant of the GMRES(m) Method Based on the Error Equations
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 19
EP - 32
PY - 2018
DA - 2018/02
SN - 2
DO - http://doi.org/10.4208/eajam.280611.030911a
UR - https://global-sci.org/intro/article_detail/eajam/10864.html
KW - Nonsymmetric linear systems, GMRES($m$) method, restart, error equations.
AB - <p style="text-align: justify;">The GMRES(m) method proposed by Saad and Schultz is one of the most
successful Krylov subspace methods for solving nonsymmetric linear systems. In this
paper, we investigate how to update the initial guess to make it converge faster, and in
particular propose an efficient variant of the method that exploits an unfixed update. The
mathematical background of the unfixed update variant is based on the error equations,
and its potential for efficient convergence is explored in some numerical experiments.</p>