Sobolev类带权函数的基于给定信息的最佳求积公式  

Best quadrature formulas based on the given information with a weight function for Sobolev class

作　　者：谢聪聪[1] 

机构地区：[1]浙江大学数学系,浙江杭州310028

出　　处：《高校应用数学学报（A辑）》2006年第2期214-222,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：给出了r阶Sobo lev类KWr[a,b]带权函数的基于给定信息的最佳求积公式和它的误差估计式.这里的给定信息是指:已知函数在给定区间若干点上的函数值和直到r-1阶导数值.对r≤2,得到了最佳求积公式和误差估计式的显式结果.另外还给出了类KW2[a,b]中在节点的导数值为零的函数所组成的子类的相应的最佳求积公式.The best quadrature formula and its errors based on the given information with a weight function for Sobolev class KW^r[a ,b] are given. The given information means that the values of a function and its derivatives up to r-1 order are given at a set of nodes on the given interval. For r≤2, explicit results for best quadrature formulas and their errors are derived. Best quadrature formula for the class KW^2[a,b],which is the subclass of KW^2[a,b] consisting of all the functions whose derivatives vanish at the fixed nodes is presented.

关 键 词：SOBOLEV类 最佳求积公式 Hermite信息 Lagrange信息 

分 类 号：O241[理学—计算数学]