Mi. 10.07.2019, Forschungsseminar Mathemtik/Physik

Thema: From values to function: interpolation and reconstruction. Referent: Prof. Dr. Claus Fieker (TU Kaiserslautern), Raum: ENC-D 308, Zeit: 14:00 Uhr c.t.

Forschungsseminar Mathemtik/Physik

From values to function: interpolation and reconstruction.

 

Mittwoch, 10.07.2019, 14:00 Uhr c.t., Raum: ENC-D 308,

Referent: Prof. Dr. Claus Fieker (TU Kaiserslautern)

 

Abstrakt:

An important approach to many problems is to use modular techniques,
followed by interpolation and possibly reconstruction techniques.
Given a (unknown) rational function f (multivariate or univariate), we're
given values of f at (suitably chosen) points. The task is then to find an
explicit rational representation: f = n/d for polynomials n and d. This
may arise in computations over a function field: here the f 's would be
the unknown coefficients of some interesting function. (For example of a
Groebner-basis of some ideal).
Using suitable points, this is reduced to a univariate rational problem.
This univariate problem is then solved via interpolation followed by rational reconstruction. Finally, the numerator and denominator polynomials
are obtained from the univariate ones.
In this talk I will explain strategies and limitations for the various steps
(sparsity, large exponents, bad evaluation points).