Finding numerical derivatives for unstructured and noisy data by multiscale kernels

Leevan LING*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

The recently developed multiscale kernel of R. Opfer [Adv. Comput. Math., 25 (2006), pp. 357-380] 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.

Original languageEnglish
Pages (from-to)1780-1800
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume44
Issue number4
DOIs
Publication statusPublished - 2006

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Inverse problems
  • L-curve
  • Multiscale kernel
  • Multivariate interpolation
  • Numerical differentiation
  • Tikhonov regularization
  • Unstructured data

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