W2^1空间中的最佳数值原函数  

THE OPTIMAL NUMERICAL PRIMITIVE FUNCTION IN THE SPACE W_2~1

作　　者：邓中兴[1] 崔明根[2] 吴勃英[2] 

机构地区：[1]哈尔滨科技大学 [2]哈尔滨工业大学

出　　处：《计算数学》1989年第2期220-224,共5页Mathematica Numerica Sinica

基　　金：国家自然科学基金

摘　　要：求数值原函数问题,是对离散形式给出的实函数u(x)(即仅给出u(x)在有限多个点上的函数值),求其近似原函数F_n(x),而且当节点无限加密时,F_n(x)收敛于u(x)的原函数F(x).例如微分方程的数值解法,实质上就归结为求数值原函数问题.By means of the regenerate kernel and the Schmidt orthorgonalization, a method for find-ing the numerical primitive function of a given function in the space W_2~1[a, b] is constructed.The uniform convergence of the approximateprimitive function to the exact one as the nodesbecome dense in [a, b] is also proved. The presented method is particularly applicable to largesystems of nodes. For small and medium scale systems of nodes, the corresponding results canstill be satisfactory because of a certain optimality of the numerical primitive function.

关 键 词：W2^1空间 数值原函数 再生核函数 

分 类 号：O241.4[理学—计算数学]