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.
出处
《计算数学》
CSCD
北大核心
1989年第2期220-224,共5页
Mathematica Numerica Sinica
基金
国家自然科学基金
