A study on multivariate interpolation by increasingly flat kernel functions
نویسندگان
چکیده
منابع مشابه
Multivariate interpolation with increasingly flat radial basis functions of finite smoothness
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.
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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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Many types of radial basis functions, such as multiquadrics, contain a free parameter. In the limit where the basis functions become increasingly flat, the linear system to solve becomes highly ill-conditioned, and the expansion coefficients diverge. Nevertheless, we find in this study that limiting interpolants often exist and take the form of polynomials. In the 1-D case, we prove that with s...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.02.006