On Quasi-Interpolation with Non-uniformly Distributed Centers on Domains and Manifolds |
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Authors: | Vladimir Maz'ya Gunther Schmidt |
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Affiliation: | Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117, Berlin, Germany |
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Abstract: | 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 hZn-lattice in Rs, sn, 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 for by a greater flexibility in the choice of generating functions used in numerical methods for solving operator equations. |
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