Abstract
Let D o be the functional given by D o f = f′(0) on C 1(−1, 1). Let Π n be the set of polynomials of degree not exceeding n and let M n be the polynomial interpolation to f at a given set of points x 1, x 2,…, x n . We approximate D o f by D o M n f. This is called a numerical differentiation formula. We study the pointwise convergence of D o M n to D o for two choices of the set of points: for equispaced points and for the extrema of the Chebycheff polynomials.
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