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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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