@Article{JICS-1-11,
author = {},
title = {A Global Property of Restarted FOM Algorithm},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {1},
number = {1},
pages = {11--20},
abstract = { In  this  paper  an  interesting  property  of  the  restarted  FOM  algorithm  for  solving  large 
nonsymmetric  linear  systems  is  presented  and  studied.  By  establishing  a  relationship  between  the 
convergence of its residual vectors and the convergence of Ritz values in the Arnoldi procedure, it is shown 
that some important information of previous FOM(m) cycles may be saved by the iteration approximates at 
the time of restarting, with which the FOM(m) cycles can complement one another harmoniously in reducing 
the  iteration  residual.  Based  on  the  study  of  FOM(m),  two  polynomial  preconditioning  techniques  are 
proposed;  one  is  for  solving  nonsymmetric  linear  systems  and  another  is  for  forming  an  effective  starting 
vector in the restarted Arnoldi method for solving nonsymmetric eigenvalue problems. 
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22855.html}
}