##
The Use of Algebraic Algorithms in Scientific Computing.

(Abstract)

Various computational tasks in Scientific Computing have a great deal of
mathematical structure which is not utilized in present algorithms for these
tasks. An obvious example is the solution of polynomial systems of equations
in many variables, as they arise in Chemistry, Mechanics,etc. Algorithms
exploiting the mathematical structure often exist within Computer Algebra, but
they rely heavily on exact rational computation.
In the presentation, it will be shown how the implementation of such
algorithms in an environment with data of limited accuracy requires a
fundamental change in some of the underlying paradigms. After the
algorithms have been redesigned in the appropriate manner, they may be
executed in floating-point arithmetic and yet produce more meaningful
results than in their original form. They can thus become part of
packages for various problem areas in Scientific Computing. Examples
will clarify the general considerations.

up