TY - JOUR
T1 - A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems
AU - Jianlei Li, Zhijiang Zhang and Liang Li
JO - Journal of Information and Computing Science
VL - 2
SP - 153
EP - 160
PY - 2024
DA - 2024/01
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22723.html
KW -  SIMPLE  preconditioner,  eigenvalue  analysis,  generalized  eigenvalue  problem,  diagonal 
scaling. 

AB -  The  eigenvalue  analysis  of  the  SIMPLE  preconditioner  for  solving  two-by-two  block  linear 
equations with the (1, 2)-block being the transpose of the (2, 1)-block and the (2, 2)-block being zero was 
investigated in Li and Vuik [Numer Lin. Alg. Appl., 2004, 11:511-523]. In this note, we extend their ideas by 
allowing the (1, 2)-block to be not equal to the transpose of the (2, 1)-block and investigate the relationship 
of  the  two  different  formulations  spectrum  of  the  SIMPLE  preconditioned  matrix  by  using  the  theory  of 
matrix eigenvalue. And also the SIMPLE type methods are given.