Computer Algebra with Data of Limited Accuracy
Date: July 19th (Friday)
Time: 14:00-14:30
Abstract
In Scientific Computing, some of the numerical data in problems
(e.g. coefficients in polynomials) have limited accuracy. The application
of standard computer algebra systems to such problems is unsatisfactory
for various reasons. An adaptation of polynomial computer algebra for data
with limited accuracy requires - first of all - a change of a fundamental
paradigm: Data spaces have to be furnished with a topology. It turns out
that a number of classical algebraic concepts (like g.c.d., Groebner bases,
etc.) are n o t continuous w.r.t. their data in situations which are
smooth w.r.t these data.
We will display various such representation singularities and exhibit their
potentially disastrous consequences for the respective algorithms. We will
also point out how this difficulty may be overcome by a suitable modification
of the conceptual approaches. The resulting algorithms are well within the
scope of computer algebra.
