Mixed Precision in CUDA Polynomial Precondition for Iterative Solver

Preconditioning technique has been used for transforming the original linear system into one which has the same solution, but likely easier to solve with an iterative solver. Using lower precision computation is a method to accelerate precondition process. We investigated mixed precision polynomial precondition both in convergence and running time on NVIDIA GPU. The numerical experiment shows that there exists a best degree for polynomial precondition, which depends on the effects of preconditioning and computation cost. And in detailed research of residual, it appears that the benefits of mixed precision precondition will lose in latter iterative steps.