数值积分的双侧逼近及应用  

Two-Sided Approximate Formule and Its Application in Numerical Integration

作　　者：刘彩艳[1] 陈兴同[1] 

机构地区：[1]中国矿业大学理学院数学系,江苏徐州221116

出　　处：《大学数学》2012年第1期61-66,共6页College Mathematics

基　　金：中央高校基本科研业务费专项资金项目(2010LKSX01)

摘　　要：通过分析基本数值求积公式的双侧逼近现象,利用加权平均的方法构造出了比原来求积公式至少高二次代数精度新的混合型求积公式,使得积分近似值精度得到大幅度提高,并给出应用它们求数值积分的具体实例.By investigating the two-sided approximation phenomenon of some basic numerical quadrature formulae, some new numerical quadrature formulae are proposed. And it is proved that the algebraic degrees of these new formulae are at least more 2 than that of the old formulae. Therefore the accuracy of new numerical quadrature formulae is greatly improved. At the end, some numerical examples are given.

关 键 词：数值求积公式 代数精度 求积余项 求积系数 求积节点 双侧逼近 

分 类 号：O241[理学—计算数学]