Remarks on the abstract theory of additive and multiplicative Schwarz algorithms - Griebel, Michael 1960-; Oswald, Peter (1993)
Abstract: "We propose a modified approach to the abstract convergence theory of the additive and multiplicative Schwarz iterative methods associated with a subspace splitting for solving symmetric positive definite linear problems. In particular, we obtain a new bound for the convergence rate of the appropriately scaled multiplicative Schwarz method directly in terms of the condition number of the corresponding additive Schwarz operator. The results may be viewed as an appendix to the recent surveys [X, Y]."
Keywords: Iterative methods (Mathematics)