Szabados, J. Optimal order of convergence of Hermite-Fejér interpolation for general systems of nodes. (English) Zbl 0810.41004 Acta Sci. Math. 57, No. 1-4, 463-470 (1993). The author studies the optimal order of convergence of Hermite-Fejér interpolation for general systems of nodes. The first result in this direction is given by the author himself in 1973. Later, Xin-Long Zhou extended this result to the case when \(X\) is the matrix of Jacobi nodes with non-positive parameters. Also, Shi worked on this order in 1991. This was the first step in proving that all Hermite-Fejér interpolations are saturated with at most of order \(O(n^{-1})\). In this paper the author makes another step by extending and strengthening the result of Shi to all polynomials. Reviewer: R.N.Siddiqi (Safat) Cited in 4 Documents MSC: 41A05 Interpolation in approximation theory Keywords:convergence; optimal order; Hermite-Fejér interpolation; nodes PDFBibTeX XMLCite \textit{J. Szabados}, Acta Sci. Math. 57, No. 1--4, 463--470 (1993; Zbl 0810.41004)