An Estimation for the Average Error of the Chebyshev Interpolation in Wiener Space

Abstract

In this paper, the first kind of Chebyshev interpolation in the Wiener space are discussed. under the L _p norm, the convergence properties of Chebyshev interpolation polynomials base on the zeros of the Chebyshev polynomials are proved. Furthermore, the estimation for the average error of the first kind of Chebyshev interpolation polynomials are weakly equivalent to the average errors of the corresponding best polynomial approximation. while p = 4, the weakly asypmtotic order $e^{4} (H_{n}, G_{4}) \approx 1 / \sqrt{n}$ of the average error in the Wiener space is obtained.