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