Construction Techniques for Highly Accurate Quasi-Interpolation Operators |
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Authors: | Robert Schaback Zongmin Wu |
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Affiliation: | aInstitut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083, Göttingen, Germany;bDepartment of Mathematics, Fudan University, 200433, Shanghai, China |
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Abstract: | Under mild additional assumptions this paper constructs quasi-interpolants in the form with approximation order ℓ−1, whereh(x) is a linear combination of translatesψ(x−jh) of a functionψinCℓ(). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the functionψ. This approach can be generalized to the multivariate setting by using discrete convolutions with tensor products of odd-degreeB-splines. |
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Keywords: | radial basis function quasi-interpolation Strang– Fix conditions smoothness order of convergence |
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