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Approximate approximations from scattered data
Dipartimento di Matematica, Università La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
2007 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 145, no 2, 141-170 p.Article in journal (Refereed) Published
Abstract [en]

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 scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by suitable polynomials such that their sum is an approximate partition of unity. For Gaussian functions we propose a method to construct the approximate partition of unity and describe an application of the new quasi-interpolation approach to the cubature of multi-dimensional integral operators. © 2006 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
2007. Vol. 145, no 2, 141-170 p.
Keyword [en]
Cubature of integral operators, Error estimates, Multivariate approximation, Scattered data quasi-interpolation
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-49952DOI: 10.1016/j.jat.2006.08.003OAI: oai:DiVA.org:liu-49952DiVA: diva2:270848
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12

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Maz´ya, Vladimir G.

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