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 language | English |
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Pages (from-to) | 1780-1800 |
Number of pages | 21 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 44 |
Issue number | 4 |
DOIs | |
Publication status | Published - 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