摘要
根据数值积分公式代数精度的定义,导出了插值型求积公式余项的具体表达式,利用此余项表达式及插值型求积公式,给出一种证明积分(不)等式的数值积分证明法,并与利用泰勒公式证明积分(不)等式的常规做法进行比较.结果表明,数值积分证明法更简洁易懂,且有规律可循,能够达到事半功倍的效果.
Based on the definition of algebraic precision of numerical integration formulas,a specific expression for computing the remainder term of interpolation-type quadrature formulas is derived.Utilizing this remainder expression and interpolation-type quadrature formulas,an effective method for proving(non-)equalities of integral is proposed,called the numerical integration proof method.Compared with the conventional approach by using the Taylor s formula to prove(non-)equalities of integral,the proposed method is not only more concise and easier to understand but also follows certain rules.It can play a multiplier effect.
作者
王茜
侯国亮
WANG Xi;HOU Guoliang(School of Mathematics,Changchun Normal University,Changchun 130032,China)
出处
《长春师范大学学报》
2025年第10期17-20,共4页
Journal of Changchun Normal University
关键词
积分(不)等式
数值积分
泰勒公式
(non-)equalities of integral
numerical integration
Taylor s formula
