查询词典 hermite interpolation 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。

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。

Osculatory Rational interpolation is similar to the polynomial Hermite interpolation, and for binary Osculatory rational interpolation, Similar to polynomial interpolation formulas haven't appeared from now on.

切触有理插值是类似于多项式插值中的Hermite插值的一种插值，而对于二元切触有理插值，目前还没有构造出类多项式的插值公式。

In this paper ,on one hand ,we establish the weakly asymptotic order of the classical Bernstein interpolation sequence approximate functionin the Wiener space(or 1-fold integrated Wiener space),on the other hand,we discuss the asymptotically order for the average error of Lagrange interpolation sequence, Hermite-Fejer interpolation sequence and Hermite interpolation sequence based on the Chebyshev nodes on the 1-fold integrated Wiener space.

本文一方面确定了经典的Bernstein多项式算子列逼近函数时在Wiener空间(或1-重积分Wiener空间)下的平均误差的弱渐近阶；另一方面确定了基于第一类Chebyshev多项式零点的Lagrange插值算子列、Hermite-Fejer插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差的弱渐近阶。

Firstly, this paper describes the history and state of the research to the minimal polynomial and the characteristic polynomial and then gives the main methods and its computational complexities for computing the characteristic polynomial and of a constant matrix, the characteristic polynomial of a polynomial matrix and the minimal polynomial of a polynomial.

本文先叙述了对最小多项式和特征多项式的国内外的研究历史和现状，然后给出了已有的计算常数矩阵特征多项式、多项式矩阵的特征多项式和常数矩阵最小多项式的主要算法及其复杂性。

On the basis of determining interpolation neighborhood, this paper factures many geochemistry plots by using more spatial interpolation of the deep penetrating geochemical data in the study area. The methods include inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, radial basis function, simple Kriging and universal Kriging, etc.

文中在确定插值邻域的基础上，应用多种空间插值方法对研究区的深穿透地球化学数据制作了多个地球化学图，如反距离加权插值法、全局多项式插值法、局部多项式插值法、径向基函数法、简单克里金法、泛克里金法等。

Romberg first use of the method is integral for integration, Then the results obtained by using the interpolation method were obtained Lagrange polynomial interpolation polynomial interpolation and Newton, re-use of least squares fitting of thinking obtained polynomial, the last of these different types of polynomial, identify their respective strengths and weaknesses.

首先运用Romberg积分方法对给出定积分进行积分，然后对得到的结果用插值方法，分别求出Lagrange插值多项式和Newton插值多项式，再运用最小二乘法的思想求出拟合多项式，最后对这些不同类型多项式进行比较，找出它们各自的优劣。

The relevant interpolation algorithms include Lagrange interpolation formula, Newton polynomial interpolation, Hermite's interpolation, cubic spline; the relevant fitting algorithms include least square method, Chebyshev multinomial fitting algorithms and so on.

主要的拟合算法有最小二乘法、切比雪夫多项式拟合算法。

Listen,point and check your answers.

听，指出并且检查你的答案。

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但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48