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On quasi-interpolation with non-uniformly distributed centers on domains and manifolds. (English) Zbl 0976.41004
Summary: The paper studies quasi-interpolation by scaled shifts of a smooth and rapidly decaying function. The centers are images of a smooth mapping of the \(h{\mathbb{Z}}^n\)-lattice in \({\mathbb{R}}^s\), \(s\geq n\), and the scaling parameters are proportional to h. We show that for a large class of generating functions the quasi-interpolants provide high order approximations up to some prescribed accuracy. Although in general the approximants do not converge as \(h\) tends to zero, the remaining saturation error is negligible in numerical computations if a scalar parameter is suitably chosen. The lack of convergence is compensated by a greater flexibility in the choice of generating functions used in numerical methods for solving operator equations.

MSC:
41A05 Interpolation in approximation theory
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