TY - JOUR
T1 - Simpler Hybrid GMRES
AU - 
JO - Journal of Information and Computing Science
VL - 2
SP - 110
EP - 114
PY - 2024
DA - 2024/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22850.html
KW - 
AB -  Hybrid GMRES algorithms are effective for solving large nonsymmetric linear systems. GMRES 
is  employed  at  the  first  phase  to  produce  iterative  polynomials,  which  will  be  used  at  the  second  phase  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,  simpler  hybrid  GMRES  algorithms  are  formulated.  It  is  described  how  to  construct  the 
iterative polynomials from simpler GMRES. The new algorithms avoid the upper Hessenberg factorization so 
that  they  are  easier  to  program  and  require  a  less  amount  of  work.  Numerical  examples  are  conducted  to 
illustrate the good performance of the new algorithms.