Accelerating Polynomial Homotopy Continuation on a
Graphics Processing Unit with Double Double and Quad Double Arithmetic
Jan Verschelde
Abstract:
Numerical continuation methods
track a solution path defined by a homotopy.
The systems we consider are defined by polynomials in several variables
with complex coefficients.
For larger dimensions and degrees, the numerical conditioning worsens
and hardware double precision becomes often insufficient to reach
the end of the solution path.
With double double and quad double arithmetic, we can solve larger
problems that we could not solve with hardware double arithmetic,
but at a higher computational cost.
This cost overhead can be compensated by acceleration on a Graphics
Processing Unit (GPU).
We describe our implementation and report on
computational results on benchmark polynomial systems.
This is joint work with Xiangcheng Yu.
the 7th International Workshop on Parallel Symbolic Computation (PASCO 2015)
the University of Bath, Bath, United Kingdom, 10-11 July 2015
slides of the talk