GPU Implementation of Inverse Iteration Algorithm for Computing Eigenvectors

Abstract

Effective GPU implementations of an inverse iteration algorithm with reorthogonalization are proposed for computing eigenvectors of symmetric tridiagonal matrices. The key to effectively accelerating the inverse iteration algorithm in GPU computing is the adoption of reorthogonalization code optimal for the GPU. The CGS2 algorithm and the compact WY orthogonalization algorithm, which can be implemented using level 2 BLAS routines, are implemented using CUBLAS. The size of the data transferred between the CPU and GPU is also optimally reduced. The proposed code of the inverse iteration algorithm using the CGS2 algorithm is shown to map well to a GPU and to achieve high performance through numerical experiments on a CPU-GPU heterogeneous computer.