Computer Science NASC Seminar

Linear Rational Interpolation Done Unwisely (But Efficiently)

Stefan Guettel, The University of Manchester

February 22, 2013 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110
(Directions)

Spring 2013 NASC Seminars Calendar

Synopsis

Polynomial interpolation to analytic functions can be very accurate,
depending on the distribution of the interpolation nodes. However, in
equispaced nodes and the like, besides being badly conditioned, such
interpolation schemes may fail to converge even in exact arithmetic.
Linear barycentric rational interpolation with the weights presented
by Floater and Hormann (Numer. Math., 2007) can be viewed as blended
polynomial interpolation and often yields better approximation in such
cases. With the help of logarithmic potential theory we derive
asymptotic convergence results for these interpolants, and we suggest
how to choose the so-called blending parameter in order to observe
fast and stable convergence, even in equispaced nodes where stable
geometric convergence is provably impossible. This talk is based on
joint work with Georges Klein (SINUM, 2012).


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