Strong Inequalities for Hermite-Fejér Interpolations and Characterization ofK-Functionals

Abstract

The works of Smale and Zhou (2003, 2007), Cucker and Smale (2002), and Cucker and Zhou (2007) indicate that approximation operators serve as cores of many machine learning algorithms. In this paper we study the Hermite-Fejér interpolation operator which has this potential of applications. The interpolation is defined by zeros of the Jacobi polynomials with parameters−1<α,β<0. Approximation rate is obtained for continuous functions. Asymptotic expression of theK-functional associated with the interpolation operators is given.