Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Multivariate quasi-interpolation schemes for dimension-splitting multiquadric

Language

English

Abstract

In this paper, we extend the multilevel univariate quasi-interpolation formula proposed in [A univariate quasi-multiquadric interpolation with better smoothness, Comput. Math. Appl., in press] to multidimensions using the dimension-splitting multiquadric (DSMQ) basis function approach. Our multivariate scheme is readily preformed on parallel computers. We show that the cost of finding the coefficient of the quasi-interpolant is 3dN on ℝd, and the work of direct evaluation of the quasi-interpolant can be reduced from 11N2 in 2D and 16N2 in 3D to ≈ 2N. A boundary padding technique can be employed to improve accuracy. Numerical results in 2D and 3D are both given. © 2003 Elsevier Inc. All rights reserved.

Keywords

Dimension-splitting, Multidimensional, Multilevel, Multiquadric (MQ), Multivariate, Quasi-interpolation, Radial basis function (RBF)

Publication Date

2005

Source Publication Title

Applied Mathematics and Computation

Volume

161

Issue

1

Start Page

195

End Page

209

Publisher

Elsevier

DOI

10.1016/j.amc.2003.12.022

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.amc.2003.12.022

ISSN (print)

00963003

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