数值算法

Keywords: BP neural networks,model approximation degree, acceptance probability, variable stepsize learning algorithm

数值结果表明该算法不仅明显地提高了BP网络的学习收敛速度，而且在一定程度上还能避免陷入局部极小。

BP neural networks ; model approximation degree ; acceptance probability ; variable stepsize learning algorithm

数值结果表明该算法不仅明显地提高了BP网络的学习收敛速度，而且在一定程度上还能避免陷入局部极小。

It is a direct scheme and can avoid accumulated error resulted by iterative methods.Value results have illustrated that our algorithm has high precision.

该方法是一种直接解法，可以减少迭代法所产生的误差积累，数值实验验证了理论分析的正确性，表明该算法具有很高的精度。

Experimental results in TiGems7.0 illustrate that this algorithm is independent of the numerical error accumulated in intersection computation, and can implement the data exchange of IGES B-rep model built by different CAD systems such as SolidWorks and Pro/E.

在TiGems7.0系统中的实验结果表明，该算法不依赖于求交运算中造成的数值误差，具有较好的鲁棒性，能够实现IGES的边界表示格式在SolidWorks，Pro/E等系统中的数据交换功能。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

A new method of American option pricing with stochastic vola...

针对随机波动率模型下美式期权定价的复杂性，本文在已有的欧式期权定价公式下，利用二叉树与随机波动率矩阵的结合，当股票价格收益波动率服从马尔可夫随机过程时，实际波动率σ下美式期权价格是随机状态波动率下价格的加权和，其权重可以由波动率矩阵算出，并且给出了对应思想的算法，最后通过数值算例进一步说明了算法的有效性。

The reactionsystem of polyesterification of DFA and EG was analyzed and simplified. Based on thehypothesis of equal and unequal activity of the end-group of monomer and polymer,the modelⅠand modelⅡfor estimating kinetic parameters were established usingimproved Genetic Algorithm, which was so improved by introducing the Elitist Model,Simulate annealing, Runge-Kutta method, proportional distribution randomizer etc.into the operators, and these models were more compatible with the estimation ofcomplex reaction kinetic model parameters.

对二聚脂肪酸与乙二醇缩聚反应体系进行了分析和简化，基于单体和聚合物端基等活性及不等活性的假设，采用已加入最优保存策略、变量数值扰动、龙格库塔积分(Runge-Kutta)算法、均匀分布的随机数发生器算子的遗传算法，建立了模型Ⅰ和模型Ⅱ，并利用C~计算机语言编程来估算动力学模型的参数。

This volume summary of the main examples of these algorithms on the basic theory and extensive analysis of the computer program design and numerical analysis of the linkages between, which is particularly noteworthy is the author of Random Number Generation procedures for processing and re-form calculation of power series.

本卷总结了主要算法范例及这些算法的基本理论，广泛剖析了计算机程序设计与数值分析间的相互联系，其中特别值得注意的是作者对随机数生成程序的重新处理和对形式幂级数计算的讨论。本书附有大量习题和答案，标明了难易程度及数学概念的使用。

Gram-Schmidt algorithm is one of the fundamental methods in linear algebra, which is mainly used to compute QR decomposition.

Gram-Schmidt正交化算法是数值线性代数中的基本算法之一，主要用于计算矩阵QR分解。

This is the University analysis of the experiment- Romberg algorithm source code, to help you learn and master the Romberg al...

· 这是大学数值分析的实验——龙贝格算法的源码，帮助大家学习和掌握龙贝格算法！

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。