Department of Mathematics
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.
Numerical differentiation, multiscale kernel, multivariate interpolation, unstructured data, inverse problems, Tikhonov regularization, L-curve
Source Publication Title
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
Ling, Leevan. "Finding numerical derivatives for unstructured and noisy data by multiscale kernels." SIAM Journal on Numerical Analysis 44.4 (2006): 1780-1800.