Computational Mathematics and Scientific Computing Seminar
Linear Rational Interpolation Done Unwisely (But Efficiently)
Speaker: Stefan Guettel, The University of Manchester
Location: Warren Weaver Hall 1302
Date: Feb. 22, 2013, 10 a.m.
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).