2018
DOI: 10.1002/nla.2172
|View full text |Cite
|
Sign up to set email alerts
|

On a Chebyshev accelerated splitting iteration method with application to two‐by‐two block linear systems

Abstract: Summary The Chebyshev accelerated preconditioned modified Hermitian and skew‐Hermitian splitting (CAPMHSS) iteration method is presented for solving the linear systems of equations, which have two‐by‐two block coefficient matrices. We derive an iteration error bound to show that the new method is convergent as long as the eigenvalue bounds are not underestimated. Even when the spectral information is lacking, the CAPMHSS iteration method could be considered as an exponentially converging iterative scheme for c… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2020
2020
2023
2023

Publication Types

Select...
5

Relationship

1
4

Authors

Journals

citations
Cited by 7 publications
(2 citation statements)
references
References 37 publications
0
2
0
Order By: Relevance
“…Other well-known preconditioning strategies for general two-by-two block matrices, such as block-triangular preconditioners, are also applicable, cf., e.g. [24,55,56]. We do not discuss them here any further.…”
Section: Remark 41mentioning
confidence: 99%
“…Other well-known preconditioning strategies for general two-by-two block matrices, such as block-triangular preconditioners, are also applicable, cf., e.g. [24,55,56]. We do not discuss them here any further.…”
Section: Remark 41mentioning
confidence: 99%
“…The PMHSS preconditioner has nearly the same workload as the PRESB preconditioner. However, it can be used in the short-term recurrence iteration methods (e.g., minimal residual method (MIN-RES) and Chebyshev semi-iteration method) [5,18,19]. The convergence of the PMHSS iteration method is analyzed when W, T ∈ R n×n are symmetric positive semidefinite matrices.…”
Section: Introductionmentioning
confidence: 99%