TY - JOUR
T1 - An Investigation of Restarted GMRES Method by Using Flexible Starting Vectors
AU - Qiang Niu & Lin-Zhang Lu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 338
EP - 351
PY - 2010
DA - 2010/03
SN - 3
DO - http://doi.org/10.4208/nmtma.2010.33.4
UR - https://global-sci.org/intro/article_detail/nmtma/6002.html
KW - Linear systems of equations, Arnoldi process, GMRES, harmonic Ritz vector.
AB - <p style="text-align: justify;">We discuss a variant of restarted GMRES method that allows changes
of the restarting vector at each cycle of iterations. The merit of
the variant is that previously generated information can be utilized
to select a new starting vector, such that the occurrence of
stagnation be mitigated or the convergence be accelerated. The more
appealing utilization of the new method is in conjunction with a
harmonic Ritz vector as the starting vector, which is discussed in
detail. Numerical experiments are carried out to demonstrate that
the proposed procedure can effectively mitigate the occurrence of
stagnation due to the presence of small eigenvalues in modulus.</p>