Using quadruple precision arithmetic to accelerate Krylov subspace methods on GPUs

Abstract

The convergence of the Krylov subspace methods is affected by round-off errors. The number of iterations until convergence may be decreased by reducing round-off errors through the use of quadruple precision arithmetic instead of double precision. We implemented the CG and BiCGStab methods using quadruple precision arithmetic and compared the performance with the standard double precision implementations on an NVIDIA Tesla K20X GPU. Our results show that in some cases our implementations using quadruple precision arithmetic outperform the double precision versions. We will show that quadruple precision arithmetic is not costly for the CG and BiCGStab methods on GPUs and the use of quadruple precision arithmetic may be a more effective alternative to the use of preconditioning. © 2014 Springer-Verlag.