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Zeitschrift für Analysis und ihre Anwendungen

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Volume 27, Issue 3, 2008, pp. 323–338
DOI: 10.4171/ZAA/1358

Published online: 2008-09-30

Approximate Approximations with Data on a Perturbed Uniform Grid

Flavia Lanzara[1], Vladimir G. Maz'ya[2] and Gunther Schmidt[3]

(1) Università di Roma La Sapienza, Italy
(2) Linköping University, Sweden
(3) Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function to the case that the data are given on a perturbed uniform grid. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible.

Keywords: Scattered data quasi-interpolation, multivariate approximation, error estimates

Lanzara Flavia, Maz'ya Vladimir, Schmidt Gunther: Approximate Approximations with Data on a Perturbed Uniform Grid. Z. Anal. Anwend. 27 (2008), 323-338. doi: 10.4171/ZAA/1358