Approximation Of The Spline

Function approximation is the modern mathematical theory of an important branch,with the development of modern science,it contains more and more extensive integration with other sciences is increasingly deepening.It not only become a calculated and applied mathmatics and optimization theory,but also with the functional analysis,differential equations,algebra, numerical analysis,harmonic analysis and wavelet analysis is closely related to such research.Spline function is derived from the general pratice of the more basic function,the past 20 years,it has gradually developed into a school in the analysis of hot topics,spline theory itself and in the numerical analysis of two has made important development,the new meaningful results still occur,particularly in the approximation theory,spline theory of the increasing status.Discussed in this paper to the Riesz base sequence for the node by the ease-spline is the most common type of spline.The history of the band limited functions in the R nodes on the use of equidistant spline interpolation functions have been discussing the issue of the relatively perfect,and then with a limited function in all aspects of development has been widely,and has made some new results.Lyubarslii and Madych research in non-equidistant nodes {x_n}_n∈Z = {....＜x_-1＜x₀＜x₁＜....} appropriate spline interpolation function.And come to a good conclusion,Chen Tung further promotion.This article is a continuation of this discussion,research in the l_p(p≥2) scale,in the two-dimensional space,the ease by splines in non-formal types of B_π,p samples on the recovery of function,and in two-dimensional space,to draw the following conclusion: ??‖f^(k)-s_2m^(k)(f)‖?? =0,k∈N∪{0},k≤m.Moreover,unifies as the approximation and the fuzzy mathematics,this article also uses to approach the method to conduct the research fuzzily to geographic information system's uncertainty,obtained approaches the method mainly to overcome the data either this or that's two value logic fuzzily,with approached the method real reflection objective reality fuzzily, obtained the result was also quite objective,scientific and the reasonable merit.