Dear Colleagues,

We continue our Colloquium.

Professor Lutai Guan, Zhongshan University, China

Bivariate Local Basis Polynomial Natural Spline Interpolation for Scattered
Data

Tuesday, November 30, 2:50 p.m. Metro 207

ABSTRACT
Since 1980's, the interpolation problem about scattered data in a plane has
been a difficulty and important problem in numerical approximation and
other fields. Many results were finished on this title. Here, we only
discuss one kind of the solving methods,which is called polynomial natural
spline interpolation.Based on the theory of spline function in Hilbert
spaces, bivariate polynomial natural splines for interpolating, smoothing
or general interpolating of scattered data over an arbitrary domain were
constructed by the one-side function. However, this method is not well
suited for large scale numerical applications. Recently, a new local
support basis of the bivariate polynomial spline space is constructed. Some
properties of this basis are also discussed.Methods to order scattered data
are shown and algorithms for bivariate polynomial natural spline
interpolation are constructed.The interpolating matrices are  sparse, and
thus, the algorithms can be easily implemented in a computer. To scattered
data in some lines, and refinement grid points interpolating, we also give
the simpler local support basis.
Boris Belinskiy
Department of Mathematics
University of Tennessee at Chattanooga
615 McCallie Ave
Chattanooga, TN 37403-2598
Ph. 423-755-4748
Fax 423-755-4586
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