GPU-Accelerated Asynchronous Error Correction for Mixed Precision Iterative Refinement

In hardware-aware high performance computing, blockasynchronous iteration and mixed precision iterative refinement are two techniques that are applied to leverage the computing power of SIMD accelerators like GPUs. Although they use a very different approach for this purpose, they share the basic idea of compensating the convergence behaviour of an inferior numerical algorithm by a more efficient usage of the provided computing power. In this paper, we want to analyze the potential of combining both techniques. Therefore, 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 correction 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.