TY - JOUR
T1 - Product Hybrid Block GMRES for Nonsymmetrical Linear Systems with Multiple Right-hand Sides
AU - 
JO - Journal of Information and Computing Science
VL - 5
SP - 303
EP - 310
PY - 2024
DA - 2024/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22829.html
KW - 
AB - Recently, the complementary behavior of restarted GMRES has been studied. We observed that 
successive  cycles  of  restarted  block  BGMRES  (BGMRES(m,s))  can  also  complement  one  another 
harmoniously in reducing the iterative residual. In the present paper, this characterization of BGMRES(m,s) 
is exploited to form a hybrid block iterative scheme. In particular, a product hybrid block GMRES algorithm 
for  nonsymmetrical  systems  with  multiple  right-hand  sides  is  proposed.  The  new  algorithm  combines  the 
advantage  of  Simoncini’s  Hybrid  Block  GMRES  and  Zhong’s  Product  Hybrid  GMRES.  Numerical 
experiments are conducted to show that the new algorithm can offer significant improvement over the hybrid 
block GMRES.