几类求积公式的统一推行及其应用

Further Extensions of Some Quadrature Rules and Application

通过构造函数Pi(t)给出了几类求积公式(辛普森公式,梯形公式,中点公式)的统一的误差估计,结果表明:推行后的求积公式误差更小,并通过举例说明了这些结果比已有文献中的结果要好。最后给出这些结果在数值积分方面的应用。

The uniform error estimation of some formulas of quadrature （such as Simpson＇s inequality, trapezoid inequality and mid-point inequality）were given by construction function. And we can see,the errors of the generalized quadrature formulas are lower. The results were better than those included in references, which was explained by some examples. Finally the results application in numerical integration was given.