@Article{JICS-1-110,
author = {},
title = {Simpler Hybrid GMRES},
journal = {Journal of Information and Computing Science},
year = {2006},
volume = {1},
number = {2},
pages = {110--114},
abstract = { Hybrid GMRES algorithms are effective for solving large nonsymmetric linear systems. GMRES 
is &nbsp;employed &nbsp;at &nbsp;the &nbsp;first &nbsp;phase &nbsp;to &nbsp;produce &nbsp;iterative &nbsp;polynomials, &nbsp;which &nbsp;will &nbsp;be &nbsp;used &nbsp;at &nbsp;the &nbsp;second &nbsp;phase &nbsp;to 
implement the Richardson iteration. In the process of GMRES, a least squares problem needs to be solved 
which involves an upper Hessenberg factorization. Instead of using GMRES, we may use simpler GMRES. 
Correspondingly, &nbsp;simpler &nbsp;hybrid &nbsp;GMRES &nbsp;algorithms &nbsp;are &nbsp;formulated. &nbsp;It &nbsp;is &nbsp;described &nbsp;how &nbsp;to &nbsp;construct &nbsp;the 
iterative polynomials from simpler GMRES. The new algorithms avoid the upper Hessenberg factorization so 
that &nbsp;they &nbsp;are &nbsp;easier &nbsp;to &nbsp;program &nbsp;and &nbsp;require &nbsp;a &nbsp;less &nbsp;amount &nbsp;of &nbsp;work. &nbsp;Numerical &nbsp;examples &nbsp;are &nbsp;conducted &nbsp;to 
illustrate the good performance of the new algorithms. 
},
issn = {3080-180X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22850.html}
}