Computer Science NASC Seminar
Algorithms Based on Analytic Function Values at Roots of Unity
Nick Trefethen, Oxford University and CIMS
September 20, 2013
10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 100121110
(Directions)
Fall 2013 NASC Seminars Calendar
Synopsis
Let $f(z)$ be an analytic or meromorphic function in the
closed unit disk sampled at the $n$th roots of unity.
Based on these data, how can we approximately evaluate
$f(z)$ or $f^{(m)}(z)$ at a point $z$ in the disk?
How can we calculate the zeros or poles of $f$ in the
disk? These questions exhibit in the purest form certain
algorithmic issues that arise across computational science
in areas including integral equations, partial differential
equations, and largescale linear algebra (e.g. the FEAST
eigenvalue code). We survey what is already known and
suggest new possibilities springing from a connection between
Cauchy integrals and rational interpolation. This is joint
work with Anthony Austin and Peter Kravanja.
