Acceleration of Hessenberg Reduction for Nonsymmetric Eigenvalue Problems Using GPU

Abstract

Solution of large-scale dense nonsymmetric eigenvalue problem is required in many areas of scientific and engineering computing, such as vibration analysis of automobiles and analysis of electronic diffraction patterns. In this study, we focus on the Hessenberg reduction step and consider accelerating it using GPU. Our main strategy is to use the CUBLAS, an optimized BLAS library for GPU. However, since Hessenberg reduction requires operations not supported by CUBLAS, we combine CPU and GPU to perform the computation. We propose two approaches for combining CPU and GPU: the one that performs as much work as possible on GPU and the one that aggressively assigns computation of small-size matrices to CPU. Experimental results show that the latter approach is considerably faster than the former. Compared with the computation on the Core i7 processor with 4 cores, the latter approach with the Tesla C1060 GPU and the Core i7 processor achieves 2.8 times speedup when computing the Hessenberg form of a 4,800 $\times$ 4,800 real matrix.