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