On the convergence of additive and multiplicative splitting iterations for systems of linear equations

Authors:
Zhong-Zhi Bai
Affiliations:
State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy o ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 3
Cited 3

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Abstract

We study convergence conditions for the additive and the multiplicative splitting iteration methods, i.e., two generalizations of the additive and the multiplicative Schwarz iterations, for Hermitian and non-Hermitian systems of linear equations, under an algebraic setting. Theoretical analyses show that when the coefficient and the splitting matrices are Hermitian, or non-Hermitian but diagonalizable, satisfying mild conditions, both additive and multiplicative splitting iteration methods are convergent, even if the coefficient matrix is indefinite.