Precondicionadores baseados na aproximação da inversa

Abstract

In this thesis we will presente a class of preconditioners based on the sparse approximation of the inverse of the coefficient matrix, for the solution of large sparse linear systems by iterative methods, Krylov methods in special. In order to make na efficient Krylov´s method solver it is extremely necessary the use of a good preconditioner. In the actual scenario, Where hybrid architectures machines are more and more common we have na increasing on the demand of highly parallel preconditioners. The sparse approximate inverse methods that will be decribed have parallel application, since its application needs Only sparse matrix-vector multiplication operations, which is a highly parallelizable kernel. Futhermore, some methods can also be constructed in parallel. The main ideia of this thesis is to presente na alternative to the traditionals preconditioners based on sparse approximation of the LU factors, which are very robust but their parallelization are nontrivial.