Multivariate interpolation with increasingly flat radial basis functions of finite smoothness

Authors:
Guohui Song;John Riddle;Gregory E. Fasshauer;Fred J. Hickernell
Affiliations:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, USA 85287;Department of Mathematics, Wheaton College, Wheaton, USA 60187;Department of Applied Mathematics, Illinois Institute of Technology, Chicago, USA 60616;Department of Applied Mathematics, Illinois Institute of Technology, Chicago, USA 60616
Venue:
Advances in Computational Mathematics
Year:
2012

Citing 6
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Abstract

In this paper, we consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in 驴 d with finite smoothness of even order converge to a polyharmonic spline interpolant as the scale parameter of the radial basis functions goes to zero, i.e., the radial basis functions become increasingly flat.