GPU-Accelerated Asynchronous Error Correction for Mixed Precision Iterative Refinement

Abstract. In hardware-aware high performance computing, block- asynchronous iteration and mixed precision iterative refinement are two techniques that are applied to leverage the computing power of SIMD accelerators like GPUs. Al-though they use a very different approach for this purpose, they share the basic idea of compensating the convergence behaviour of an inferior numerical al-gorithm by a more efficient usage of the provided computing power. In this paper, we want to analyze the potential of combining both techniques. There-fore, we implement a mixed precision iterative refinement algorithm using a block-asynchronous iteration as an error correction solver, and compare its performance with a pure implementation of a block-asynchronous iteration and an iterative refinement method using double precision for the error cor-rection solver. For matrices from the University of Florida Matrix collection, we report the convergence behaviour and provide the total solver runtime using different GPU architectures