Acceleration of Hessenberg Reduction for Nonsymmetric Eigenvalue Problems in a Hybrid CPU-GPU Computing Environment

Communicated by Yasuaki Ito 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 in a hybrid CPU-GPU computing environment. Considering that the Hessenberg reduction algorithm consists almost entirely of BLAS (Basic Linear Algebra Subprograms) operations, we propose three approaches for distributing the BLAS operations between CPU and GPU. Among them, the third approach, which assigns small-size BLAS operations to CPU and distributes large-size BLAS operations between CPU and GPU in some optimal manner, was found to be consistently faster than the other two approaches. On a machine with an Intel Core i7 processor and an NVIDIA Tesla C1060 GPU, this approach achieved 3.2 times speedup over the CPU-only case when computing the Hessenberg form of a 8,192 × 8,192 real matrix