Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

The recently developed multiscale kernel of R. Opfer is applied to approximate numerical derivatives. The proposed method is truly mesh-free and can handle unstructured data with noise in any dimension. The method of Tikhonov and the method of L-curve are employed for regularization; no information about the noise level is required. An error analysis is provided in a general setting for all dimensions. Numerical comparisons are given in two dimensions which show competitive results with recently published thin plate spline methods.

Publication Year

2006

Journal Title

SIAM Journal on Numerical Analysis

Volume number

44

Issue number

4

Publisher

Society for Industrial and Applied Mathematics

First Page (page number)

1780

Last Page (page number)

1800

Referreed

1

DOI

10.1137/050630246

ISSN (print)

00361429

Keywords

Numerical differentiation, multiscale kernel, multivariate interpolation, unstructured data, inverse problems, Tikhonov regularization, L-curve

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