On the Enlarged Krylov Subspace Method: SRE-CG2

Abstract

We are interested in solving sparse systems of linear equations Ax=b with Krylov subspace methods. A new approach for reducing communication in Krylov subspace methods was introduced that consists of enlarging the Krylov subspace by a maximum of t vectors per iteration, based on a domain decomposition of the graph of A. We think of the solution as belonging to the enlarged Krylov subspace which is a superset of the Krylov subspace. Several enlarged conjugate gradient versions that converge faster than CG in terms of iterations were introduced, such as MSDO-CG and SRE-CG2 and SRE-CG. In this thesis we introduce a variant of SRE-CG2: flexible SRE-CG2 and test its effectiveness in terms of iterations and time for convergence as compared to SRE-CG2.