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On approximation of functions and their derivatives by quasi-Hermite interpolation. (English) Zbl 0842.41017
Summary: We consider the simultaneous approximation of the derivatives of the functions by the corresponding derivatives of quasi-Hermite interpolation based on the zeros of $$(1- x^2) p_n (x)$$ (where $$p_n (x)$$ is a Legendre polynomial). The corresponding approximation degrees are given. It is shown that this matrix of nodes is almost optimal.
##### MSC:
 41A25 Rate of convergence, degree of approximation 41A05 Interpolation in approximation theory 41A28 Simultaneous approximation
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