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On Quasi-Interpolation with Non-uniformly Distributed Centers on Domains and Manifolds

✍ Scribed by Vladimir Maz'ya; Gunther Schmidt

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
177 KB
Volume
110
Category
Article
ISSN
0021-9045

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✦ Synopsis

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 Z n -lattice in R s , s 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 for by a greater flexibility in the choice of generating functions used in numerical methods for solving operator equations.

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