求积公式

After the boundary integral operator is decomposed into the sum of a monotonous Hammerstein operator and a compact mapping by the Sidi rule, we construct the nonlinear discrete equations.

积分算子被分解成单调的Hammerstein算子和一个紧算子后，运用Sidi求积公式，建立了非线性离散方程组。

Then interpolating cubature formulae is given based on Lagrange interpolation formulae. Secondly it make use of the cubature formula on the triangle to construct cubature formulae on the correspondent spherical triangle.

通过把其定义域上的积分化为平面单纯形{u =(u1， u2， u3)： u1 + u2 + u3 = 1， u1， u2， u3〉0}上的积分，然后利用平面单纯形上数值积分公式给出其在球面三角形上的对d次齐次多项式精确成立的Gauss求积公式的构造方法。

The main purpose is to construct cubature formulae on an arbitrary spherical triangle. Firstly a method for accurately computing the definite integral of spherical polynomial functions on a spherical triangle is proposed.

本文主要研究定义在球面三角形上函数的数值积分，通过积分的插值多项式函数构造具有多项式精度的插值型求积公式，以及给出精确计算球面三角形上多项式函数方法。

The formula requires not only the function value,but also the first derivative and second derivative value on node.

此类求积公式不但需要结点上的函数值，还需要结点上的一阶和二阶导数值。

Boley and Golub used Gauss quadrature formula to solve the inverse problem, but I used other different methods and thoughts. I obtained a new decomposition form of orthogonal matrix consisted by the unit eigenvectors of Jacobi matrix and found the direct relations between the first row and the orther rows of this orthogonal matrix.

Boley和Golub的算法是用高斯求积公式，而本人另辟蹊径，推出了关于Jacobi矩阵单位特征向量组成的正交阵的一种分解形式，并找到此正交阵第一行和其它行的直接联系，由此避免了通过求特征多项式计算尾主子阵的特征值，得到了新的稳定解法。

By means of the Hermite interpolation formula with second derivative,a type of integrating formulas with second derivative is derived.

利用带二阶导数的Hermite插值公式，导出一类具有二阶导数的求积公式。

Measurement method can directly measure the diameter and length of the mathematical quadrature formula.

测定的方法可直接量其直径和长度用数学求积公式计算。

Report : Programming Environment : Newton MATLAB7 K polynomial interpolation procedures to achieve Romberg of Quadrature program Gaussian out PCA Elimination of the program.

计算方法实验报告：编程环境：MATLAB7.0 牛顿K次插值多项式的程序实现龙贝格求积公式的程序实现高斯列主元消去法的程序实现。

Report : Programming Environment : Newton MATLAB7 K polynomial interpolation procedures ...

计算方法实验报告：编程环境：MATLAB7.0 牛顿K次插值多项式的程序实现龙贝格求积公式的程序实现高斯列主元消去法的程序实现。

The author successfully applies the Gauss-type integral formula to the numerical solution to the constant differential equation and creates the Gauss-type implicit Runge-Kutta Method of which the accuracy of order 4 and degree 7 is already equivalent to that of the RK method with order 10 and degree 8 that is in common use.

成功地将高斯型求积公式用于常微分方程的数值解中，得到了高斯型隐式龙格库塔方法，4级7阶 GRK 法的精度已与目前较为常用的10级8阶 RK 法的精度相当。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。