Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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.

Keywords

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

Publication Date

2006

Source Publication Title

SIAM Journal on Numerical Analysis

Volume

44

Issue

4

Start Page

1780

End Page

1800

Publisher

Society for Industrial and Applied Mathematics

Peer Reviewed

1

DOI

10.1137/050630246

Link to Publisher's Edition

http://dx.doi.org/10.1137/050630246

ISSN (print)

00361429

Share

COinS