GPU Accelerated Polynomial Spectral Transformation Methods

Abstract

A new class of methods for accelerating linear system solving and eigenvalue computations for positive definite matrices using GPUs is presented. This method makes use of techniques from polynomial approximation theory to construct new types of polynomial spectral transformations that are easy to parallelize and when combined with GPUs can give a factor of 100 reduction in run times for certain matrices. These methods also require significantly less memory than traditional methods, making it possible to solve large problems on an average workstation.