查询词典 approximation theorem

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

According to the characteristic that the definition point of the Q matrix of wave front is always located on the extremum point on the axis of the beam, a three-dimensional formula for the rectificative factor of phase in complex ray paraxial approximation is proposed, which calculates the rectificative factor of phase directly without considering the calculation of the main directions and curvatures and the rotation of the coordinates, thus simplifying the paraxial approximation calculation by the complex ray expansion method.

根据波前Q矩阵的定义点总位于波束轴上极值点的特点，提出了三维复射线近轴近似相位校正因子计算公式。该公式不用考虑主方向和主曲率的计算和坐标旋转，直接计算相位校正因子，从而简化了复射线展开法的近轴近似计算。

The difference of results under two approximations-high order approximation and paraxial approximation are also given.

最后用计算机绘制了列阵成像系统中各观察面上的场强分布。

The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group..

这些方法主要涉及如无规相近似、平均场理论(aka 鞍点或半经典理论)、虚时间中的隧道动力学、瞬子、贝里相、相干态路径积分及重整化群等概念。

A neural network is then used to represent the estimation of potentials,both the parameterized TD(0) learning formulas and algorithm are also derived for approximating the policy evaluation.By the approximation values of potentials and approximation policy iteration,a unified neuro-dynamic programming optimization approach is consequently proposed for both two criteria.

根据定义式，建立性能势在平均和折扣性能准则下统一的即时差分公式，并利用一个神经元网络来表示性能势的估计值，导出参数TD(0)学习公式和算法，进行逼近策略评估；然后，根据性能势的逼近值，通过逼近策略迭代来实现两种准则下统一的神经元动态规划(neuro-dynamic programming，NDP)优化方法。

By analysing the compute result of the quadratic approximation formula, we educe the conclusion that 3 is the best rank code for the quadratic approximation formula.

通过对最小二乘拟合公式实际计算结果的分析，得出了"拟合公式阶数取3为最佳"的结论。

Simulation results indicate that the proposed wavelet network in the paper has a good approximation capability, and has the advantages of rapid convergence rate and high approximation accuracy.

结果表明，这种新的小波网络具有良好的函数逼近能力，收效速度快且逼近精度高。

With regard to the accuracy and smoothness of a set of discrete data points approximation, this paper gave a whole fairing and approximation algorithm of cubic Non-Uniform Rational B-Spline curve.

针对离散数据点序列的拟和精度及光顺度问题，提出了一种三次非均匀有理B样条曲线整体光顺逼近算法。

The two methods of model simplification are presented for large scale systems, they are the least square approximation and the rational fraction approximation.

本文针对大系统的频域模型简化提出了两种方法：最小二乘近似法和有理分式近似法。

The use of the rational approximation and the Rayleigh quotient leads to that the quality of power-series expansion is significantly improved and the range of approximation is extended with a few of additional operation counts.

在只增加少许计算量的情况下，利用向量值函数的有理逼近方法以及 Rayleigh 商来改善摄动解的逼近质量并扩大其逼近范围。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。