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arXiv · 1611.05001

Minimal Numerical Differentiation Formulas

Oleg Davydov·Robert Schaback
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Abstract

We investigate numerical differentiation formulas on irregular centers in two or more variables that are exact for polynomials of a given order and minimize an absolute seminorm of the weight vector. Error bounds are given in terms of a growth function that carries the information about the geometry of the centers. Specific forms of weighted $\ell_1$ and weighted least squares minimization are proposed that produce numerical differentiation formulas with particularly good performance in numerical experiments.

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Oleg Davydov, Robert Schaback. 2018-05-22. Minimal Numerical Differentiation Formulas. https://arxiv.org/abs/1611.05001

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