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, 10012-1110
(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 large-scale 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.


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