Subspace correction methods in algebraic multi-level frames

Abstract

This study aims at introducing new algebraic multi-level solution techniques for linear systems with M-matrices. Previous optimal geometric constructions by multi-level generating systems or multi-level frames are adapted. The new contribution is a purely algebraic construction of multi-level frames. A new class of algebraic multi-level algorithms is derived by applying subspace correction iterative solvers to the algebraic multi-level linear system. These algorithms feature error resilience properties and potential massive parallelism. The proposed work outperforms previous geometric constructions since a black-box, geometry-independent methodology is considered. Moreover, optimality results of geometric constructions are matched. Overall, the new method will be well suited for generic linear algebra libraries for future multi- and many-core systems.