查询词典 approximation theorem

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

在Schur定理的指导下，许多关于Schur定理的推论便产生了，并且形成了一个完整的Schur定理理论体系，把Schur定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

For the given endpoint interpolation conditions, a new approximation method of multidegree reduction is presented. Using Chebyshev polynomial approximation theory, the nearly best uniform approximation under the interpolation conditions of endpoints can be obtained.

对于给定的首末端点的各阶插值条件，给出了一种新的一次降多阶逼近算法，应用Chebyshev多项式逼近理论达到了满足端点插值条件下的近似最佳一致逼近。

Applying the Euler method to the equation and particularly using the interpolation technique on variable delay, the Euler approximation is obtained. The discrete Euler approximation is extended to the continuous Euler approximation. It is proved that the Euler numerical solutions will converge strongly to the true solution under the local Lipschitz condition.

对方程应用欧拉方法，特别地对变延迟部分运用插值技巧进行数值离散后，将离散的欧拉格式延拓为连续的欧拉格式，从而得到欧拉格式在局部Lipschitz条件下强收敛到解析解。

The moving least squares approximation makes only require least squares approximation with regard to functional value on all nodes. It makes no require for the residual of derivative approximation.

移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小，对近似函数导数的误差没有任何约束。

After introducing the primary approximation approaches for curve and surface offset, we give an optimal approximation approach for offsetting curve based on shifting control points, which relies on approximating the normal by Legendre polynomial approximation.

在全面介绍了等距曲线曲面逼近的主要方法以后，作者首先利用Legendre多项式得到基曲线法矢曲线的最佳平方逼近，由此给出了基于控制顶点偏移的等距曲线最优逼近的算法，它在算法效果和效率上都远优于其他同类算法。

This paper firstly established a general mathematical model for the approximation to gradient and suggested two optimization principles of the approximation model,and then developed two optimal algorithms to reach minimum anisotropy or minimum approximation error while...

提出了通用梯度近似算法的数学模型和两种优化准则，进而推导出两种梯度近似的优化算法。

The main work of the thesis consists of summarizing the characteristics of the approximation methods,compiling the programs of approximation methods,and getting availability of every approximation method according to examples.

本文的主要工作是总结各种近似方法的特点，编写各近似方法的程序，通过算例总结出各种近似方法的适用性。

It can adjust time interval in light of approximation effect, and the current segment's approximation error is not influenced by other segments'. This method can improve approximation precision of reach set and makes the verification applicable in practical systems.

该方法可根据近似误差自动调节近似时所用的时间间隔，每段的近似误差不受其它段的影响，达到提高近似精度和减少计算量的目的，从而进一步降低验证方法实现的难度。

In the final chapter, we discuss interval polynomial approximation of rational surfaces. Firstly, we briefly state the interval-surface approximation based on the Taylor Expansion, and later, we give out a better interval-surface approximation based on the optimization method, which is also the main work of this paper.

第四章主要介绍了有理曲面的区间多项式的逼近，首先简单介绍了基于泰勒展开来做的区间曲面逼近，后面是本文的主要工作，我们基于优化方法得到了更好的区间曲面逼近，它也是本文的重要部分。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。