On the fundamental polynomials for Hermite–Fejér interpolation of Lagrange type on the Chebyshev nodes

Abstract

For a fixed integer and , let denote the th fundamental polynomial for Hermite–Fejér interpolation on the Chebyshev nodes . (So is the unique polynomial of degree at most which satisfies , and whose first derivatives vanish at each .) In this paper it is established that It is also shown that is an increasing function of , and the best possible bound so that for all , and is obtained. The results generalise those for Lagrange interpolation, obtained by P. Erdős and G. Grünwald in 1938.

Keywords

• Hermite–Fejér interpolation
• Lagrange interpolation
• Polynomial interpolation
• Chebyshev nodes