Computational and Applied Math Proseminar

Friday, March 23, 1:40 p.m. GWC 604

Jean-Paul Berrut
Dept. Math., University of Fribourg

A Formula for the Error of Finite Sinc-Interpolation over a Fixed Finite Interval

Abstract Sinc-interpolation is an infinitely smooth interpolation on the whole real line based on a series of shifted and dilated sinus--cardinalis functions used as Lagrange basis. It often converges very rapidly, so for example for functions analytic in an open strip containing the real line and which decay fast enough at infinity. This decay does not need to be very rapid, however, as in Runge's function 1/(1+x^2). Then one must truncate the series, and this truncation error is much larger than the discretization error (it decreases algebraically while the latter does it exponentially).

In our talk we will give a formula for the error committed when merely using function values from a finite interval symmetric about the origin. The main part of the formula is a polynomial in the distance between the nodes whose coefficients contain derivatives of the function at the extremities.

For further information please contact: mittelmann@asu.edu