关于Gauss-Lobatto积分公式问题的一个注记  

Remarks on the Gauss-Lobatto quadrature formula

作　　者：刘春[1] 林京[1] 

机构地区：[1]合肥工业大学数学系,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2008年第5期815-816,共2页Journal of Hefei University of Technology：Natural Science

摘　　要：Gauss-Lobatto积分公式对次数不超过2n-1次的多项式是准确地成立的。最近,有人以积分上下限作为额外的变元来进一步极小化公式误差的方法以改进这个公式,并给出了计算直到2n+1次单项式的数值例子,但是既没有分析误差,又没有对积分区间的长度加以限制;文章中给出了这种改进的一个误差上界,此误差上界随着积分区间长度趋向零而减小到零,说明他们的改进实际上是不恰当的。It is well known that the Gauss-Lobatto quadrature rule is exact for polynomials of degree at most 2n-1. Recently some researchers improved such a quadrature and further minimized the error by means of using integral bounds as additional variables, and offered some numerical examples for monomials of degree up to 2n＋1, but neither analyzed the error bounds nor restricted the length of the integral interval. In this paper, an upper error bound for such improvements is given. Such an error bound vanishes as the length of the integral interval approaches zero, which shows that their im- provement is actually improper.

关 键 词：Gauss-Lobatto积分 求积公式 误差分析 

分 类 号：O241.1[理学—计算数学]