Research Seminar - Andreas Löhne
We are pleased to announce the upcoming Research Seminar on Oktober 7, 2022.
The Institute for Statistics and Mathematics is pleased to invite you to the next research seminar, taking place on campus:
Andreas Löhne (Department of Mathematics, Friedrich Schiller University Jena)
On convex polyhedron computations using floating point arithmetic
Friday, October 7, 2022, 10:30 am, Building TC, Room TC.3.01
Convex polyhedra are not necessarily finite sets but they can be finitely represented. Thus they play an important role for various types of set computations, for instance in set optimization. Most of the computational techniques for polyhedra rely in some sense on vertex enumeration, which means to compute the vertices and extremal directions of a polyhedron which is given by (finitely many) linear inequalities. The inverse problem, which is equivalent by polarity, is called convex hull problem. In practice it is quite common to implement vertex enumeration and convex hull methods by using floating point arithmetic. However, in most situations there is no proof of correctness of the methods when inexact arithmetic is used. In particular, there is no correct practicable floating point algorithm known for polytopes of dimension larger than 3. We demonstrate by examples that inexact computations can produce results which are far away from the correct ones. We present an approximate vertex enumeration method, which is shown to be correct for polytopes of dimension 2 and 3. We discuss why a generalization to any higher dimension is, if possible, not trivial.
Please note the start time of 10:30 am.
We aim to stream all on-campus talks via Zoom. A direct link to the stream will be posted on our website.
For further information and the seminar schedule, please see: