A two‐step matrix splitting iteration paradigm based on one single splitting for solving systems of linear equations

For solving large sparse systems of linear equations, we construct a paradigm of two‐step matrix splitting iteration methods and analyze its convergence property for the nonsingular and the positive‐definite matrix class. This two‐step matrix splitting iteration paradigm adopts only one single split...

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Bibliographic Details
Published inNumerical linear algebra with applications Vol. 31; no. 3
Main Author Bai, Zhong‐Zhi
Format Journal Article
LanguageEnglish
Published Oxford Wiley Subscription Services, Inc 01.05.2024
Subjects
Asymptotic methods
Convergence
convergence property
iteration method
Iterative solution
Linear equations
Linear systems
Mathematical analysis
Matrices (mathematics)
matrix splitting
Splitting
system of linear equations
two‐step scheme
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Summary:For solving large sparse systems of linear equations, we construct a paradigm of two‐step matrix splitting iteration methods and analyze its convergence property for the nonsingular and the positive‐definite matrix class. This two‐step matrix splitting iteration paradigm adopts only one single splitting of the coefficient matrix, together with several arbitrary iteration parameters. Hence, it can be constructed easily in actual applications, and can also recover a number of representatives of the existing two‐step matrix splitting iteration methods. This result provides systematic treatment for the two‐step matrix splitting iteration methods, establishes rigorous theory for their asymptotic convergence, and enriches algorithmic family of the linear iteration solvers, for the iterative solutions of large sparse linear systems.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2510