Parallel Polynomial Evaluation

Jan Verschelde and Genady Yoffe

Abstract:

Fast polynomial evaluation (and its derivatives) is a critical component in Newton's method and in continuation methods for solving polynomial systems. In the path trackers of PHCpack, we have integrated the software library QD-2.3.9 for double double and quad double complex arithmetic to increase the accuracy of the computations. To offset the extra cost of the multiprecision arithmetic we use multiple cores. In particular, we calculate quality up factors, answering the question: if we have c cores available, how many extra digits d can we use in the working precision keeping the wall clock time fixed?

SIAM Conference on Parallel Processing for Scientific Computing Savannah, 15-17 February 2012.

slides of the talk