On massively parallel algorithms to track one path of a polynomial homotopy

Jan Verschelde

Abstract:

The latest generation of graphics processors delivers one Tflop of peak performance but requires massively parallel algorithms occupying thousands of threads. In previous work we obtained good speedups for two building blocks to run Newton's method: the evaluation and differentiation of polynomial systems, and the solving of linear systems in the least squares sense, using double double and quad double arithmetic. This talk will present a massively parallel algorithm to track one solution path of a homotopy defined by a polynomial system.

This is joint work with Genady Yoffe and Xiangcheng Yu.

2013 SIAM Conference on Applied Algebraic Geometry, Minisymposium on Algorithms in Numerical Algebraic Geometry, 1-4 August 2013, Fort Collins, Colorado.

slides of the talk