Abstract
The paper discusses the error estimate of Wu-Schaback's quasi-interpolant for a wider class of approximated functions (the functions with lower smoothness order). Three cases are considered: a function with a Lipschitz continuous first-order derivative, a continuous function and a Lipschitz continuous function, respectively.
Highlights
Introduction operator LDN −2Quasi-interpolation methods have been used widely in data∑ (LD f )(x) = f0α0(x) + f1α1(x) + f jψ j(x) + fN −1αN −1(x) + fNαN (x), j=2 analysis, and have great values in theory and in many where application areas such as medicine, geology, economy and computer science
We discuss the convergence of operator LD f for a wider range of approximated functions
We use two theorems showed by Beatson and Powell [4], and our method differs from that in [6]
Summary
In 1994, Wu and Schaback proposed the quasi-interpolation Interpolation schemes and discussed the convergence of the schemes.= αN−1(x) In 1994, Wu and Schaback [6] proposed a useful quasi-interpolation (x N − x) − φN −1(x) − φN −1(x) − φN −2 (x) , 2(x N − x N −1) We discuss the convergence of operator LD f for a wider range of approximated functions
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