Reformulated Conjugate Gradient for the Energy-Aware Solution of Linear Systems on GPUs

In this paper we introduce a redesign of the conjugate gradient method for the iterative solution of sparse linear systems on heterogeneous systems accelerated by graphics processing units (GPUs). Reshaping the GPU kernels induced by the classical formulation of the CG method into algorithm-specific routines results in a slight increase of performance and, more importantly, enables the efficient exploitation of power-saving techniques implicit in the hardware, like the processor C-states, that produce remarkable energy savings. Numerical experiments using data matrices from a popular sparse matrix collection show that the time overhead naturally associated with the application of these energy-aware techniques is no longer crucial to the overall runtime performance.