Finding Numerical Derivatives for Unstructured and Noisy Data by Multiscale Kernels

Leevan Ling*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)
21 Downloads (Pure)


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
Issue number4
Publication statusPublished - 26 Sept 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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