On approximation of functions and their derivatives by quasi-Hermite interpolation. (English) Zbl 0842.41017

Min, G.

Int. J. Math. Math. Sci. 19, No. 2, 279-286 (1996).

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

Keywords:

optimal nodes; Legendre polynomials; best approximation; Hermite interpolation; derivatives