查询词典 polynomial approximation

Structure-Based Approximation Learning Theory: Under the description of manifold and topological architecture of neural field, we have proposed a learning frameworks of neural networks based on global architecture approximation theory borrowed from the concept of topology and manifold to solve the optimal problems of learning in non-nonlinear and non-Euclidean space, and discussed a few basic components of the learning theory, learning mechanism and learning algorithm in the term of structure-based approximation and global structure analysis.

基于结构的逼近学习理论：通过人工神经网络模型神经场的流形结构和拓扑结构描述，我们提出了在非线性和非欧氏空间中基于整体结构逼近的神经场学习理论框架；用对偶流形理论和拓扑概念作为工具，讨论了神经网络的学习理论、学习机理、学习算法和算法的具体实现。

Direct and inverse theorems of approximation by this kind of operators are discussed, and the Jackson—type integral estimation of approximation and Steckin — Marchaud inequality of weak type of uniform approximation for these operators are obtained.

讨论了一元Bernstein型算子的逼近正逆定理，建立了该算子逼近的Jackson型积分估计式和一致逼近的弱Steckin-Marchaud型不等式。

And the direction query efficiency based on multi-approximate index is compared with that based on taditional external approximation index. 2 The algorithms of nearest neighbor and reverse nearest neighbor about point, line and ploygen based on multi-approximate index are proposed after the virous methods of distance measure are discussed in detail. And the query efficiency of NN and RNN based on multi-approximate index is compared with that based on taditional external approximation index. 3 The basic concept of semi-join and the strategy of distance-direction semi-join are introduced. And the model of distance relationship, direction relationship and the bounding for spatial object are discussed. Then the method is presented about how to implement the query of distance-direction semi-join, and the efficiency of the algorithm based on multi-approximate index is compared with that based on taditional external approximation index.

即：1在方向关系矩阵模型、开域方向模型基础上，讨论了基于多重近似索引下的定性与定量方向检索方法，并通过实验对基于多重近似索引与外部近似索引下的方向检索效率进行了对比分析；2详细讨论了各种距离度量方法，提出了基于多重近似索引下的点、线、面的最邻近查询和反最邻近查询算法，并通过实验对基于多重近似索引与外部近似索引下的最邻近查询和反最邻近查询效率进行比较分析；3介绍了半连接的基本概念，探讨了距离关系、方向关系以及空间对象数量的约束模型，给出了基于多重近似索引下的距离方向半连接实现方法，并通过实验对基于多重近似索引与外部近似索引下的距离方向半连接的效率进行了比较分析。

Comparing to the algebraic polynomial,the trigonometric polynomial interpolation studying is more difficult ,and the methods are more different.

与代数多项式相比，三角多项式插值的研究要困难一些，研究方法也有众多不同。

In the linear algebraic the coefficient of polynomial and the corresponding relation of the farmnla of multi-line matrix could be built,thus seck the maximum common factor of the polynomial through making use of primary transformation of line.

在线性代数中，可以建立多项式的系数与多行矩阵表示式之间的对应关系，从而利用初等行变换求多项式的最大公因式。

The basic idea is as follows: first, a kind of plane α-B-spline interpolation curve with a shape control parameter a is constructed; then, by converting the first derivatives of the curve into Bernstein polynomial, the positive conditions of Bernstein polynomial can be used to get the necessary and sufficie nt conditions for the monotonicity of α-B-spline interpolation curves, i.e., the range of the parameter a. Therefore, monotone-preserving interpolating curves can be obtained succinctly.

其基本思想是：首先构造带有形状可调参数的一类平面(-B样条插值曲线，再把其一阶导矢的两个分量分别转化为Bernstein多项式，从而利用Bernstein多项式的正性条件，得到此曲线为单调的充要条件，即形状参数的取值范围，简单、快捷地实现此参数样条曲线的保单调插值。

It included Karaji's binomial theorem and rules of the arithmetic polynomial operations and developed Karaji's theory of polynomial.

其中保存了凯拉吉的关於二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。

This book included Karaji's binomial theorem and rules of the arithmetic polynomial operations and it developed Karaji's theory of polynomial.

算术珍本》中保存了凯拉吉的关于二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。

When the determinant is expanded, it produces a polynomial, called the characteristic polynomial

当行列式展开后，得到一个多项式，叫它为特征多项式。

The differential characteristic set for differential polynomial system maintains the essential character of original differential polynomial system.

微分多项式系统的微分特征列集保留了原微分多项式组的本质特征，具有三角化良序结构等优点，能够克服不同领域问题中的一些困难。

"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。