The Error Estimates Of Operator Approximation

Operator approximation has been always one of central issues studied,with the development of functional analysis, probabilistic statistics, computational methods and so on, the studying for operator approximation has also taken a new step. In recent years, many researchers on approximation theory have studied the problem of operator approximation in a few probability measure spaces. Due to special construction principles and methods of interpolation operators,they provide effective computational tools for many complex computational problems, and have become the object which many scholars study in this area. At present,major average errors of operator approximation are studied in the Wiener measure space and in Brownian bridge measure space.however,to1-fold integrated Wiener space,the related paper is fewer. Therefore, we mainly discuss average errors of Grunwald interpolation operator sequence and Hermite interpolation operator sequence in1-fold integrated Wiener space.Mainly following aspects:Firstly, it introduces the relevant concepts and the nature of the measure space.Secondly,in1-fold integrated Wiener space, based on the Chebyshev nodes of the first kind, the paper discusses the average error of approximation of Grunwald interpolation operator sequence without endpoint. Based on the Chebyshev nodes of the second kind,discusses average errors of approximation of Grunwald interpolation operator sequences without endpoint and with endpoint,the results show that approximation orders of Grunwald interpolation operator sequences without endpoint based on the Chebyshev nodes of the first kind and with endpoint based on the Chebyshev nodes of the second kind are consistent,but based on the Chebyshev nodes of the second kind, approximation of Grunwald interpolation operator sequences with endpoint is emanative.Thirdly,in1-fold integrated Wiener space, based on the Chebyshev nodes of the first kind, It discusses the average error of approximation of Hermite interpolation operator sequence,its results superior to corresponding Grunwald interpolation operator sequence.