Mixed precision iterative refinement methods for linear systems: convergence analysis based on krylov subspace methods

Authors:
Hartwig Anzt;Vincent Heuveline;Björn Rocker
Affiliations:
Institute for Applied and Numerical Mathematics 4, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany;Institute for Applied and Numerical Mathematics 4, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany;Institute for Applied and Numerical Mathematics 4, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Venue:
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Year:
2010

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Abstract

The convergence analysis of Krylov subspace solvers usually provides an estimation for the computational cost. Exact knowledge about the convergence theory of error correction methods using different floating point precision formats would enable to determine a priori whether the implementation of a mixed precision iterative refinement solver using a certain Krylov subspace method as error correction solver outperforms the plain solver in high precision. This paper reveals characteristics of mixed precision iterative refinement methods using Krylov subspace methods as inner solver.