We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.
|Original language||English (US)|
|Number of pages||22|
|Journal||Numerical Linear Algebra with Applications|
|State||Published - Nov 11 2014|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work was supported in part by the National Science Foundation through grant DMS-0609544. It was also supported in part by award number KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
ASJC Scopus subject areas
- Algebra and Number Theory
- Applied Mathematics