查询词典 polynomial approximation

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

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。

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。

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。

ABSTRACT This paper summarizes our researches on two key techniques in curve and surface modeling-the geometric approximation techniques and the geometric interpolation techniques. The former includes three types of geometric approximation techniques: Hybrid polynomial approximation to rational curves and surfaces, offset curves and surfaces approximation, interval Bézier curves and surfaces approximation. The latter includes a series of algorithms for shape blending modeling: the MSI algorithm for shape blending between space polylines or trees, the MSI algorithm for shape blending between triangular meshes, and skeleton-based shape blending algorithms using triangular decomposition and star-shape decomposition.

本文是作者对曲线曲面造型中两类核心技术几何逼近技术和几何插值技术的研究成果的总结，其中前者包括有理曲线曲面的Hybrid多项式逼近、等距曲线曲面逼近和区间曲线曲面逼近等三类几何逼近方法；后者包括用于形状混合造型的几何插值方法的一系列算法：空间多边形形状混合的MSI插值算法、三角网格形状混合的MSI插值算法、树的形状混合的MSI插值算法以及基于骨架树形状混合的三角剖分算法和星形剖分算法。

It is proved that if'sparse NP complete sets under polynomial-time Turing reductions exist'then 'SAT is polynomial-time non-adaptively search reducible to decision', and that if 'P is not equal to NP'then either'SAT is not polynomial-time non-adaptively search reducible to decision'or'SAT is not polynomial-time truth-table reducible to bounded approximable sets', and that if'P is not equal to NP'then'sparse complete sets for NP under polynomial-time disjunctive reductions do not exist'.

因为用现有的证明技术不可能绝对地解决这个假设，本文研究了这个假设与其他关于SAT结构性质的假设之间的关系，证明了如果'NP有多项式时间图灵归约下的稀疏完全集'则'SAT是多项式时间并行地搜索归约为判定'，以及如果假设'P不等于NP'，则要么'SAT不是多项式时间并行地搜索归约为判定'，要么'SAT不能用多项式时间真值表归约归约为有界可近似集'。

When to get the coefficients of polynomial directly,the ill-conditioned matrix may be produced and effect the precision of result.Using orthogonal polynomial can avoid this problem.This paper introduces 4 orthogonal polynomial.In our discussion,it is proposed to use Chebyshev polynomial and Legendre polynomial,they are easier to sa...

讨论4种常用正交多项式在拟合卫星轨道与时间函数时的适用性；通过计算实例说明利用切比雪夫多项式和勒让德多项式做数据拟合时具有很高的精度；分析得出评定多项式拟合数据精度的适用阶数，实际应用中可降低工作量，提高计算效率；最后讨论同一多项式阶数下不同历元数对拟合结果的影响。

A new method that transforms bitlevel waveform polynomial to word-level polynomial model is given, allowing for simple composition This method offers an efficient way to determine whether two descriptions from different design levels are equivalent, so component reuse, synthesis and verification across design levels can be realized. In addition, an experimental system using C language is established, including modules such as representation of waveform polynomial, decision of path senstization, delay computing, clocking based on single-period sensitization, clocking based on multi-period sensitization, test generation considering noise and transformation from bit-level waveform polynomial to word-level polynomial model. They respectively used to test models and techniques proposed in this paper.

另外，基于C语言本人设计开发了一个实验软件系统，该系统包括波形多项式表示模块、敏化通路判定模块、延时计算模块、单周期敏化的最小时钟周期精确确定模块、多周期敏化的最小时钟周期确定方法模块、考虑噪声的测试生成模块和位级波形多项式描述转化成字级多项式描述模块，分别用于对本文各章中提出的自动化设计的模型和方法进行实验验证。

The second part has summarized from the one-dimension and multivariate respects the abundant approximation properties of Bernstein polynomials, mainly including the estimation of approximation degree, derivative approximation, linear combination approximation and weighted approximation.

第二部分从一元和多元两个方面系统总结了Bernstein算子丰富的逼近性质，主要包括逼近度估计、导数逼近、线性组合逼近和加权逼近等。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。