A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
A cross difference approach to the analysis of subdivision algorithms
Neural, Parallel & Scientific Computations
Numerical Methods, Software and Analysis
Numerical Methods, Software and Analysis
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Fast Implementation of Scale-Space by Interpolatory Subdivision Scheme
IEEE Transactions on Pattern Analysis and Machine Intelligence
The use of higher order finite difference schemes is not dangerous
Journal of Complexity
Stable numerical differentiation for the second order derivatives
Advances in Computational Mathematics
Differentiation by integration with Jacobi polynomials
Journal of Computational and Applied Mathematics
Error analysis of Jacobi derivative estimators for noisy signals
Numerical Algorithms
Hermite spectral and pseudospectral methods for numerical differentiation
Applied Numerical Mathematics
Automatica (Journal of IFAC)
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Some new formulae for numerical differentiation and integration are derived by using interpolatory subdivision algorithms. These interpolatory subdivision algorithms are originally designed for the generation of smooth curves. The main advantage of these numerical formulae is that they produce better numerical results if the data comes from functions with fractal-like derivatives. The main disadvantage of these formulae is that they normally do not have the best approximation orders. By using different interpolatory subdivision algorithms, higher order approximation formulae can be obtained. Some numerical examples are given to compare these formulae with the traditional high accuracy formulae.