[Vortraege] Nachtrag Vortragsankündigungen KW. 20

[Danijela Radosavljevic]

Sehr geehrte Fakultätsmitglieder,

anbei ein Nachtrag der Vortragsankündigungen für diese Woche.

Mit freundlichen Grüßen

Danijela Radosavljevic

Mittwoch, 19. Mai 2010, 15:00 Uhr bis 15:45 Uhr, Olga Taussky-Todd Raum 
(C 209), UZA 4
Junior Kolloquium
Privatdoz. Dr. M. Kauers (RISC, Linz)
„Exact Linear Algebra in Real Life “

Abstract: In principle, computing the nullspace of a matrix is not a
difficult thing to do. Gaussian elimination provides a simple
algorithm which settles the problem completely and requires just
a cubic number of operations. But in practice, if the
coefficients of the system at hand are exact rational numbers or
even polynomials in one or more indeterminates, the actual
performance of classical Gaussian elimination can be much worse
than the theory suggests. As a matter of fact, software packages
like Maple or Mathematica sometimes already have difficulties
solving systems of size 50x50 or so within a reasonable amount of
time. If a dense linear system with thousands of unknowns is to
be solved exactly, it is advisable to switch to finite fields,
where computations can be done quickly, and then to reconstruct
the rational solution from its homomorphic images. Also this
technique was already known to Gauss, and it is nowadays a
standard tool in all areas of computer algebra. We will explain
it for the special situation of solving linear systems.

Dekan Univ.-Prof. Dr. Harald Rindler, V.-Prof. Mag. Dr. Herwig Hauser