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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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