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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.
41A25 Rate of convergence, degree of approximation
41A05 Interpolation in approximation theory
41A28 Simultaneous approximation
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