Approximation by Radial Basis Functions with Finitely Many Centers
نویسنده
چکیده
Interpolation by translates of \radial" basis functions is optimal in the sense that it minimizes the pointwise error functional among all comparable quasi{interpolants on a certain \native" space of functions F . Since these spaces are rather small for cases where is smooth, we study the behavior of interpolants on larger spaces of the form F 0 for less smooth functions 0. It turns out that interpolation by translates of to molli cations of functions f from F 0 yields approximations to f that attain the same asymptotic error bounds as (optimal) interpolation of f by translates of 0 on F 0 . AMS Classi cation: 41A15, 41A25, 41A30, 41A63, 65D10
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