Adaptive version of Simpler GMRES

Abstract. In this paper we propose a stable variant of Simpler GMRES by Walker and Zhou [15]. It is based on the adaptive choice of the Krylov subspace basis at given iteration step using the intermediate residual norm decrease criterion. The new direction vector is chosen as in the original implementation of Simpler GMRES or it is equal the normalized residual vector as in the GCR method. We show that such adaptive strategy leads to a well-conditioned basis of the Krylov subspace and we support our theoretical results with illustrative numerical examples.

• Type: Journal
• Year: 2010
• Where: NA
• Authors: Pavel Jiránek, Miroslav Rozlozník
• Keywords: Krylov Subspace, Krylov Subspace Basis, NA 2010, Simpler GMRES