On the Convergence Rate of Hermite-Fejér Interpolation

By the Peano kernel theorem, this paper establishes the convergence rates for Hermite-Fejer interpolation with the observed function values and its first derivatives at Gauss-Jacobi pointsystems. These error bounds share that for a function analytic in the Bernstein ellipse \(\mathcal {E}_{\rho }\), the error decays exponentially; while for a functions of finite regularity, the error decays depending on the regularity.