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来源：百度知道 编辑：UC知道 时间：2024/06/14 10:35:40
For the integral of the form ,where is a given nonnegative and integrable function with which is know as the weight function ,a mechanical quadrature formula is an approximation to it by a linear combination of values of at distinct points selected on ,i.e, ,where which is called the quadrature sum , .we call the remainder of the quadrature formula(2).
We may arbitrarily choose the nodes ’s and the coefficients ’s ,in as much as the structure of the mechanical quadrature formula is arbitrary .certainly,we hope that(2)will possess the certain accuracy for the class of polynomials through the choice of ’s and ’s. let ,which is called the node polynomial of .
The following fact is obvious: 1 ,It is a classical result that the formula(2)can ,by a judicious choice of the nodes ’s and the coefficients ’s,be made exact for all polynomials of degree at most 2n-1.Formula of this type is usually known as Gaussian quadrature formula. The choice of nodes and c
We may arbitrarily choose the nodes ’s and the coefficients ’s ,in as much as the structure of the mechanical quadrature formula is arbitrary .certainly,we hope that(2)will possess the certain accuracy for the class of polynomials through the choice of ’s and ’s. let ,which is called the node polynomial of .
The following fact is obvious: 1 ,It is a classical result that the formula(2)can ,by a judicious choice of the nodes ’s and the coefficients ’s,be made exact for all polynomials of degree at most 2n-1.Formula of this type is usually known as Gaussian quadrature formula. The choice of nodes and c
为积分的形式，是一种给予和非负积函数与知道，这是由于重量的功能，机械求积公式是一个近似给它的线性组合的价值在不同的点，选定的，即，这是所谓的正交总之，我们要求的其余部分，求积公式（ 2 ） 。
我们可以任意选择节点' S和系数奇摩，在高达结构力学求积公式是武断的。当然，我们希望（ 2 ）将拥有一定的准确性，为类多项式，通过选择' S和'美国让，即所谓的节点多项式。
以下的事实是显而易见的：一，它是一个古典的结果，该公式（ 2 ） ，可以由一个明智的选择，节点' S和系数奇摩，作出确切的所有多项式的程度，最多为2 n - 1 。公式，这类型的通常称为高斯求积公式。选择节点和系数为高斯求积公式是独特的和其节点都必须选择适当的，虽然它possdsses最高precision.there是一种求积公式，节点可任意选择与系数取决于他们只，这种thay是确切的所有多项式的程度，最多的N - 1.quadrature公式，这种类型是人所共知的，作为插值类型。在本文件中，我们会介绍一种求积公式（ 1 ）被视为准-高斯型高斯求积公式和求积公式，插值tupe只是其中两个极端的情况下，准高斯求积公式。这类正交公式已讨论了许多作者[ 1 〜 6 ] ，它发挥了重要作用数值解奇异积分方程。
让一指类的所有多项式的程度不大于N和方面一如果n < 0 。
我们成立1其中1是Lagrange插值多项式。我们呼吁，如正交公式正交公式内插类型。显然，他们的系数完全取决于节点和1个