A Gpu Implementation of the Filtered Lanczos

This paper describes a graphics processing unit (GPU) implementation of the Filtered Lanczos Procedure for the solution of large, sparse, symmetric eigenvalue problems. The Filtered Lanczos Procedure uses a carefully chosen polynomial spectral transformation to accelerate the convergence of the Lanczos method when computing eigenvalues within a desired interval. This method has proven particularly effective when matrix-vector products can be performed efficiently in parallel. We illustrate, via example, that the Filtered Lanczos Procedure implemented on a GPU can greatly accelerate eigenvalue computations for certain classes of symmetric matrices common in electronic structure calculations and other applications. Comparisons against previously published CPU results suggest a typical speedup of a factor of 10.