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Numerical algorithms based on analytic function values at roots of unity

Abstract:

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. We anal...

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Anthony P. Austin More by this author
Peter Kravanja More by this author
Lloyd N. Trefethen More by this author
Publication date:
2013-07-05
URN:
uuid:f58b4eb8-94f3-4afd-bc32-8edf44835927
Local pid:
oai:eprints.maths.ox.ac.uk:1733

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