查询词典 Hermite polynomial

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。

The work in this thesis is based on continued fraction theory. Combining continued fractions with polynomial functions, we construct a new osculatory continued fraction interpolation—osculatory rational Hermite-like interpolation. Its representation is simpler than that of Hermite polynomial interpolation and its computation is concise since the continued fractions coefficients can be worked out by using Viscovatov algorithm.

与之相关的理论成果不断地推陈出新，本文就是在连分式理论的基础上做了相应的工作，将多项式和连分式相结合，构造了一种新的切触有理插值——类Hermite切触有理插值，新的插值方法在表示形式上比传统的切触有理插值更直观，并且通过引入Viscovatov算法，切触插值连分式的系数求解得以简化。

Polynomial smooth techniques are applied to SVM model and replace x+ by a very accurate smooth approximation that is Hermite Interpolation polynomial,thus the undifferential model is converted into a differential model.The deduction procedure of Hermite Interpolation polynomial smoothing x+ is extended.

三次Hermite插值多项式光滑的支持向量机模型采用的是一种多项式光滑技术，用三次Hermite插值多项式代替单变量函数x+，将原来不可微的模型变为可微的模型，并且给出了三次Hermite插值多项式光滑化单变量函数x+的推导过程。

On the basis of deformation Hermite polynomial, secondary Schmidt orthogonal method and combination algorithm work together to generate UWB pulse.

在变形Hermite多项式的基础上，将二次Schmidt正交化算法与组合算法结合，使得生成的脉冲不仅正交，而且具有很高的频谱利用率。

Applying the Hermite polynomial expansion, this integral-differential equation is creatively transformed into deterministic differential equation.

创造性地使用Hermite多项式展开，将确定性的积分——微分方程转换为确定性的微分方程。

For reactor, the point reactor kinetics equation with six-group delayed neutrons is used and influence of coolant's and fuel's temperature is considered, conduction model of one dimension and single-channel model is used in thermal and hydraulic calculation, third-order Hermite polynomial is used to solve the point reactor kinetics equation.

对于反应堆，在物理计算中采用了带有六组缓发中子的点堆方程，同时考虑了多普勒效应及冷却剂温度效应对反应性的影响；在热工水力计算中采用了一维的热传导模型与单通道模型；在求解点堆方程中采用了Hermite插值的方法，克服了点堆方程的刚性问题。

The close relationship between the Hybrid polynomial approximation and the classical Hermite polynomial approximation to rational curves and surfaces are studied, Hermite approximation is in fact a special case of Hybrid approximation. The sufficient and necessary condition for the convergence of Hybrid approximation to rational Bézier surface is deduced and proved.

围绕着有理曲线曲面的Hybrid逼近，作者研究了有理曲线曲面的Hybrid多项式逼近与传统的Hermite多项式逼近之间的密切关系，并指出Hermite逼近事实上是Hybrid逼近的一种特例，此后演绎并证明了有理Bézier曲面的Hybrid多项式逼近收敛的充分必要条件。

With some modifications of Laplace\'s approximation,we obtain uniform asymp-totic formulas for the Stieltjes-Wigert polynomial,the q~(-1)-Hermite polynomial and the q-Laguerre polynomial.

通过将Laplace逼近方法做一些改进，我们得到一些关于Stieltjes-Wigert多项式，q~(-1)-Hermite多项式和q-Laguerre多项式的一致渐近公式。

Keywords : AFSA;neural network;coupling regress model of projection pursuit;projection direction;threshold;Hermite polynomial

应用神经网络的投影寻踪耦合回归模型存在优化问题，学习过程中运用人工鱼群算法进行优化，进而获得最佳的投影方向、阈值和正交Hermite多项式系数。

Due to the limited number of measurements on the response data, both Kalman Estimator technique and Singular Value Decomposition incopoerated with piecewise cubic Hermite Polynomial curve fitting method are used to reconstruct the unmeasured reponses and establish the full response measurement.

由於有限的量测资料，本文介绍卡氏重建器与结合分段式立方Hermite型插值多项式之奇异值分解重建法，以重建未量测点之反应历时，以利进行部分量测系统之外力识别。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失