An optimal block iterative method and preconditioner for banded matrices with applications to PDEs on irregular domains. (English) Zbl 1252.65068
The authors present a completely algebraic version of the Schwarz method, including an algebraic approach to finding the optimal operator or a sparse approximation thereof. The method is applied to any banded or block banded systems of linear equations. The authors prove that the optimized Schwarz method converges in two iterations. Numerical examples are also presented and discussed.
Reviewer: Răzvan Răducanu (Iaşi)
MSC:
65F10 | Iterative numerical methods for linear systems |
65F08 | Preconditioners for iterative methods |
65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |