Accelerating Path Tracking for Polynomial Homotopies

Jan Verschelde

Abstract:

Polynomial homotopies define deformations of polynomial systems. Path tracking methods apply numerical predictor-corrector techniques to compute solutions starting at known solutions in the homotopy. As the number of variables and degrees of the polynomials grow, the standard double precision becomes insufficient for accurate results. Aiming to compensate for the cost of double double and quad double arithmetic we apply massively parallel algorithms to accelerate the tracking of solution paths on the NVIDIA Tesla C2050 and K20C.

This is joint work with Xiangcheng Yu.

2014 SIAM Conference on Parallel Processing for Scientific Computing, 18-21 February, Portland, Oregon, USA

slides of the talk