On the approximation of functions and their derivatives by Hermite interpolation

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

“…In the case of Hermite interpolation, a theorem on extreme nodes was established by the authors that agreed with Pottinger's results [32] and was an improvement of the results obtained in [25]. Pottinger [33] used the Chebyshev nodes to prove that the convergence condition depends on the norms of H 2n+1 . The author also proved that the growth of the operator norms is of n th order:…”

Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials

“…Using Theorems 1 and 2, we havehere . By (1.1) and the formula (see, Pottinger 1978, p. 272),where is the best approximation to , we haveIn view of , using Jackson’s theorem (Natanson 1965, p. 86), we havewhich completes the proof of Theorem 3. …”

“…Before we state our theorem, we define where is the space of all polynomials of degree . (this definition is stated in Pottinger 1978, p. 272).…”

A generalization of Hermite interpolation

“…( cos(2nj)0, sin(2n-j)0, Similarly, using the identity sin nora sin nOk + sin join sin jOk 3=1 k,m 1, rt, (3 6) we can prove (3 4) satisfies (3 ,5S,(.f, COSOk) ,5f(cosOk) (k 1,...,n)…”