Construction Techniques for Highly Accurate Quasi-Interpolation Operators
نویسندگان
چکیده
Under mild additional assumptions this paper constructs quasi -interpolants in the form f h (x) = +1 X j= 1 f(hj)' h x h j ; x 2 IR; h > 0 (0.1) with approximation order ` 1, where ' h (x) is a linear combination of translates (x jh) of a function in C ` (IR). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the function . This approach can be generalized to the multivariate setting by using discrete convolutions with tensor products of odd-degree B{splines. AMS classi cations: 41A15, 41A25, 41A30, 41A63, 65D10.
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