Minimal numerical differentiation formulas

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 $$\ell _1$$ℓ1 and weighted least squares minimization are proposed that produce numerical differentiation formulas with particularly good performance in numerical experiments. The results are of interest in particular for meshless generalized finite difference methods as they provide a consistency error analysis for such methods.

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