Soft error resilient QR factorization for hybrid system with GPGPU

Abstract

The general purpose graphics processing units (GPGPU) are increasingly deployed for scientific computing due to their performance advantages over CPUs. As a result, fault tolerance has become a more serious concern compared to the period when GPGPUs were used exclusively for graphics applications. Using GPUs and CPUs together in a hybrid computing system increases flexibility and performance but also increases the possibility of the computations being affected by soft errors. In this work, we propose a soft error resilient algorithm for QR factorization on such hybrid systems. Our contributions include (1) a checkpointing and recovery mechanism for the left-factor Q whose performance is scalable on hybrid systems; (2) optimized Givens rotation utilities on GPGPUs to efficiently reduce an upper Hessenberg matrix to an upper triangular form for the protection of the right factor R, and (3) a recovery algorithm based on QR update on GPGPUs. Experimental results show that our fault tolerant QR factorization can success- fully detect and recover from soft errors in the entire matrix with little overhead on hybrid systems with GPGPUs.