##### Department of Mathematics,

University of California San Diego

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### Computational and Applied Mathematics Seminar

## Jean-Paul Berrut

#### University of Fribourg \\ Switzerland

## 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 discretisation error (it decreases algebraically while the latter does it exponentially). \vskip0.5em In our talk we will give a formula for the error commited 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.

Host: James Bunch

### April 10, 2007

### 11:00 AM

### AP&M 5402

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