Multivariate interpolation with increasingly flat radial basis functions of finite smoothness
نویسندگان
چکیده
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 R 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.
منابع مشابه
Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions
Multivariate interpolation of smooth data using smooth radial basis functions is considered. The behavior of the interpolants in the limit of nearly flat radial basis functions is studied both theoretically and numerically. Explicit criteria for different types of limits are given. Using the results for the limits, the dependence of the error on the shape parameter of the radial basis function ...
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ورودعنوان ژورنال:
- Adv. Comput. Math.
دوره 36 شماره
صفحات -
تاریخ انتشار 2012