Homotopy continuation methods apply predictor-corrector algorithms to solve polynomial systems. Our implementation on a Graphics Processing Unit (GPU) combines algorithmic differentiation with double double and quad double arithmetic. Our experiments with GPU acceleration show that we can offset the cost overhead of double double precision arithmetic. We report on our implementation on the NVIDIA K20C and the integration into the software PHCpack and phcpy.
The SIAM Conference on Parallel Processing for Scientific Computing. Universite Pierre et Marie Curie, Paris, France, 12-15 April 2016.