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.

[1]  Michael Garland,et al.  Implementing sparse matrix-vector multiplication on throughput-oriented processors , 2009, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis.

[2]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[3]  Peter K. Kitanidis,et al.  Multipreconditioned Gmres for Shifted Systems , 2016, SIAM J. Sci. Comput..

[4]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[5]  Mei Han An,et al.  accuracy and stability of numerical algorithms , 1991 .

[6]  Bing Yang,et al.  BiELL: A bisection ELLPACK-based storage format for optimizing SpMV on GPUs , 2014, J. Parallel Distributed Comput..