The L 2 - Approximation Orders of Principal Shift - Invariant Spaces Generated by a Radial Basis Function
نویسنده
چکیده
Approximations from the L 2 -closure S of the nite linear combinations of the shifts of a radial basis function are considered, and a thorough analysis of the least-squares approximation orders from such spaces is provided. The results apply to polyharmonic splines, multiquadrics, the Gaussian kernel and other functions, and include the derivation of spectral orders. For stationary re nements it is shown that the saturation class is trivial, i.e., no non-zero function in the underlying Sobolev space can be approximated to a better rate. The approach makes an essential use of recent results of de Boor DeVore and the author.
منابع مشابه
Approximation Orders of and Approximation Maps from Local Principal Shift-invariant Spaces Approximation Orders of and Approximation Maps from Local Principal Shift-invariant Spaces
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