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Colloquium, Spring 2004

Day: Thursday April 29 Time: 4:00pm Place: BH 227 Title: B-splines and the Schoenberg-Whitney Theorem Speaker: Ben Casler Abstract: Piecewise polynomials are frequently used to interpolate data and model functional relationships. B-splines form a convenient basis for the space of all piecewise polynomials. Their useful properties include a high-degree of differentiability and ease of use in computations. We will briefly review polynomial data interpolation techniques, motivating the development of B-splines. We show how the values, derivatives, and integrals of linear combinations of B-splines can be easily computed. We present the Schoenberg-Whitney Theorem which provides necessary and sufficient conditions for interpolation by B-splines. We examine the error associated with B-spline interpolation, developing a result analogous to the Weierstrass Approximation Theorem. An application to the Runge function will demonstrate the benefits of B-spline approximations over non-piecewise interpolating polynomials. This talk should be accessible to undergraduates who have taken Math 304 or Math 375. Cookies: In BH 300 at 3:30pm thanks to Tjalling.