The Average Error Of The Interpolation Operator Sequence In Function Probability Space

Interpolation theory is a mathematical theory,old but fashionable.Its abundant theories and advanced methods provide powerful and fruitful tools for solving compute problems.The aver-age error of interpolation operator sequence in a few function probability spaces is very impor-tant.Major work about the average error of interpolation operator sequence is only discussed in Wiener space at present,however,to the function probability space whose covariance kernel is the reproducing kernel of W₂¹[0,1]and the Brownian bridge measure space,the related paper is so few.With the methods of discussing average error in Wiener space,we discuss the average error of Hermite-Fejér and Lagrange interpolation operator sequence in two function probability spaces. At first,we discuss the average error of Egervary-Turan Hermite-Fejér interpolation operator se-quence based on the extended zeros of Chebyshev polynomial of the first kind in the wiener space, then we discuss the average error of Lagrange and Hermite-Fejér interpolation operator sequence in an important function probability space,we discuss the average error of Lagrange triangle inter-polation operator sequence in Brownian bridge measure space in the end of this paper.According to the content,we divide it into four chapters.In the first chapter,we give the preface.In the second chapter,we establish the weakly asymptotic order of the average error of Egervary-Turan Hermite-Fejér interpolation operator sequence based on the extended zeros of Chebyshev polynomial of the first kind in the wiener space.In the third chapter,we establish the weakly asymptotic order of the average error of the La-grange and Hermite-Fejér interpolation operator sequence which are based on the first Chebyshev nodes in the space whose covariance kernel is the reproducing kernel of W₂¹[0,1].In the fourth chapter,we establish the weakly asymptotic order of the average error of the Lagrange triangle interpolation operator sequence which is based on the equivalence nodes in the Brownian bridge measure space.