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

By Zhong-Zhi Bai. 2003

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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.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7ad183328ad02f1d5246f7b76efc7057041e11ec