Graduate Computational Algebraic Geometry Seminar
Jan Verschelde
UIC
Quality Up in Polynomial Homotopy Continuation
Abstract: Homotopy continuation methods to solve polynomial systems scale well on
parallel computers, but their reliability and accuracy is often in doubt
because of their reliance on floating-point arithmetic.
In a recent joint work with Genady Yoffe we experimentally determined
using QD-2.3.9 (a software library of Y. Hida, X.S. Li, and D.H. Bailey)
that the overhead of double double arithmetic compared to working with
ordinary doubles is of the same magnitude as computing with complex numbers.
With multiple cores we can compensate for this overhead
and thus achieve a so-called quality up.
In particular, with 8 cores we can compute more accurately with double
doubles in roughly the same time as in standard double precision.
Similar factors apply to quadruple the working precision.
This talk will address how the quad doubles of QD-2.3.9 are integrated
and applied in the software package PHCpack to solve larger polynomial
systems more accurately.
Thursday November 11, 2010 at 10:00 AM in SEO 1227