Mixed Precision Error Correction Methods for Linear Systems: Convergence Analysis based on Krylov Subspace Methods

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 error correction 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 error correction methods using Krylov subspace methods as inner solver.