ylfink@water.waterloo.edu (ylfink) (09/13/88)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
SCIENTIFIC COMPUTATION SEMINAR
- Thursday, September 22, 1988
Dr. M.D. Buhmann, Department of Applied Mathematics and
Theoretical Physics, University of Cambridge, will
speak on ``Cardinal Interpolation with Radial Basis
Functions''.
TIME: 4:00 PM
ROOM: DC 1304
ABSTRACT
For a radial-basis-function phi : R -> R we consider
interpolation on an infinite regular lattice
n
If(x) = sum f(k) chi (x-k), x member of R ,
n
k member of Z
n
to f : R -> R, where the cardinal function
n
chi (x) = sum c phi (||x-k||), x member of R ,
n k
k member of Z
n
satisfies chi (j) = delta for all j member of Z . We address the
oj
question of existence of such cardinal functions chi for
a class of radial-basis-functions which includes
2q+1 2q 2 2
phi (r) = r , phi (r) = r log r, phi (r) = sqrt r + c and
2 2
phi (r) = 1 sqrt r + c where q member of Z . It is shown that
+
- 2 -
cardinal interpolation for all these radial-basis-
functions is feasible and that that cardinal functions
chi yield surprisingly good localization properties.
Thus we conclude that cardinal interpolation with
radial-basis-functions is a highly promising approach
to multivariate interpolation.
An introductory talk on radial function approximation
will be given in DC 1304 at 3:30 pm. on Friday,
September 16, 1988.
September 13, 1988