Global errors for approximate approximations with Gaussian kernels on compact intervals
The method of approximate approximations [see \textit{V. Mazýa} and \textit{G. Schmidt}, Approximate approximations. Mathematical Surveys and Monographs. 141. Providence, RI: AMS (2007; Zbl 1120.41013)] is applied to a function defined on a compact interval. After convenient extension of \(f\in C^k[-1,\,1]\) \((k=0,\,1,\,2)\) on \([-1.5,\,1.5]\), \(f\) is approximated by quasi-interpolation on equally spaced nodes with translates of the Gaussian kernel. The authors present error estimates in the uniform norm and this result extend to the corresponding approximation of \(f \in C([-1,\,1]^2)\).
scientific article; zbMATH DE number 5804929