A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems
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@Article{JICS-5-153,
author = {Jianlei Li, Zhijiang Zhang and Liang Li},
title = {A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {5},
number = {2},
pages = {153--160},
abstract = { 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.
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22723.html}
}
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.
Jianlei Li, Zhijiang Zhang and Liang Li. (2024). A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems.
Journal of Information and Computing Science. 5 (2).
153-160.
doi:
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