切比雪夫多项式

采用切比雪夫多项式法和Floquet理论相结合来预测铣床运行中的颤振和分岔，得到了颤振稳定性极限图。

The shifted Chebyshev polynomials and Floquet theory are adopted for the prediction chatter stability and bifurcation in milling . The stability lobes diagram is obtained .

差分进化算法（DE）是由RainerStorn和KennethPrice为求解切比雪夫多项式而于1996年共同提出的一种采用浮点矢量编码在连续空间中进行随机搜索的优化算法。

Differential Evolution ( DE ) by Rainer Storn and Kenneth Price for solving Chebyshev Polynomials in 1996 jointly proposed a vector-encoded using floating-point margin continued space random search optimization algorithm .

在GPS数据处理中，对相位观测值周跳的解算及卫星轨道坐标的拟合推算，切比雪夫多项式是比较好的算法之一。

For determination of cycle slips of GPS phase measurements and calculation of satellite orbital coordinates in GPS data processing the Chebyshev polynomial is a good method .

对作为兴波阻力计算核函数的Green函数的单、双积分项分别采用特殊函数展开、切比雪夫多项式逼近的方法进行计算，提高了计算速度。

In the single and double integral terms of Green function , the kernel function of wave-making resistance expression , Special function expansion method and Chebyshev polynomial approach method have been adopted respectively , which greatly increase the calculation speed .

由切比雪夫多项式的最佳一致逼近的性质可以得到n阶Wang-ball曲线的最佳一致逼近曲线，并得到其最优的逼近精度。

Because of the best uniform approximation property of Chebyshev polynomial , the best uniform approximation curve of the Wang-ball curve can be got , and it had the best precision too .

利用切比雪夫多项式使矛盾方程组系数矩阵正交化，利用Householder变换直接解矛盾方程组，尽可能降低病态条件数，提高了计算精度。

The coefficient matrix is orthogonalized by using polynomial and the overdetermined equations are solved by Householder transformation . The numerical ill-condition is decreased as low as possible , hence the operational accuracy is increased .

经研究表明，运用EM算法能挖掘出观测数据的潜在数据，弥补因数据量不够切比雪夫多项式需要降阶处理的不足，提高了卫星坐标计算的精度。

The research shows that the EM algorithm can dig out the potential data of observation data , then make up for the deficiency that chebyshev polynomial must reduce the order because of the lack data , finally improve the precision of satellite orbit coordinates . 3 .

切比雪夫多项式在磨耗形踏面设计中的应用

Application of Chebyshev Polynomials on the Design of Worn Tread Profile

有关两类切比雪夫多项式的几个关系式

Several relations between Chebyshev polynomials of the first and second kind

切比雪夫多项式拟合方法在车辆导航应用中的研究

The Research of Chebyshev Polynomials ' Fitting Applied in Vehicle Navigation

基于复杂曲线表示的切比雪夫多项式拟合并行算法

Chebyshev Multinomial Approximation Parallel Algorithm Based on Complex Curve Representation

二类切比雪夫多项式积和的几个组合恒等式

Some identical relations about the sum of Chebyshev polynomials product

切比雪夫多项式逼近在大地测量计算中的应用

The Application of Chebyshev Polynomial Approximation in Geodetic Calculation

利用切比雪夫多项式建立液压元件模型

Modelling hydraulic components by use of Chebyshev polynomial

求非线性动力系统周期解的切比雪夫多项式法

Chebyshev Polynomials : a useful method to get the periodic solution of nonlinear dynamics

用切比雪夫多项式方法分析支承在颈轴承上的裂纹转子的稳定性

Analysis of the Stability of a Cracked Rotor Supported on Journal Bearings via Chebyshev Polynomials

两类新的切比雪夫多项式

Two New Kinds of the Tchebycheff polynomials

辛变换与切比雪夫多项式

Symplectic transformation and chebyshev polynomial

切比雪夫多项式的混沌性

Chaos of the Tchebycheff polynomial

利用母函数的方法，研究了第一类和第二类切比雪夫多项式，分别得到二类切比雪夫多项式积和式的几个有趣的恒等式。

The author studied the first and second kind of Chebyshev polynomials , and obtained some identical equations .

通过实例分析了利用广播星历的轨道参数、拉格朗日多项式插值和切比雪夫多项式拟合这三种方法计算卫星任意时刻的坐标，并进行了精度比较。

In this paper calculates GPS satellite coordinates separately using orbit parameter of GPS broadcast ephemeris , Lagrange polynomial insert and Chebyshev polynomial fitting , and their calculation precisions are compared .

本文首次定义和推导了移位切比雪夫多项式（第一类和第二类）的分离矩阵，它具有简洁的递推关系和三角形结构。

The separative matrices of shifted Chebyshev polynomials of the first and second kinds , which have a nice structure and an elegant recursive formula , are introduced at the first time .

本文主要阐述切比雪夫多项式的一个重要应用，利用切比雪夫多项式能减少近似多项式的项数而不降低其精度，并给出了具体方法。

This paper presents an important application of Chebyshev polynomial Its concrete content is to decrease number of terms of approximate polynomial without reducing the degree of precision and give a concrete method .

在计算中用切比雪夫多项式分段拟合均匀大地电磁响应的反函数，并给出一套系数，由此算出的视电阻率误差小于1%。

A set of Chebyshev polynomial coefficients for calculating the full wave resistivity is given . The maximum relative error in the polynomial fitting is less than one percent in the apparent resistivity .

文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组，采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组。

By use of integral transform and integral equation , the singular integral equations of this problem are derived , which are transformed into a set of algebraic equations by means of contour integral and Chebyshev polynomials expanding techniques .

提出了另3种可以用于解算周跳及卫星轨道坐标拟合的正交多项式，并利用实测数据进行了解算，取得与切比雪夫多项式相同的结果。

In addition , other 3 orthogonal polynomials for determining the cycle slips and calculating the satellite orbital coordinates are proposed . A practical resolution of some measured data with these polynomials has been done and the results are the same as with Chebyshev polynomial .

本文针对信号处理中一类常用的非线性模型，提出了切比雪夫正交多项式神经网络（TOPNN）。

For a common kind of nonlinear in signal processing , Tchebycheff Orthogonal Polynomial Neural Network ( TOPNN ) is put forward in the paper .

切比雪夫逼近多项式在非线性电路中的应用

Application of Chebyshev Approximate Polynomial to the Analysis of Nonlinear Circuit

同时比较了自然正交展开方法与切比雪夫正交多项式展开方法的收敛速度。

And then the convergent velocity is compared between the EOF and Orthogonal polynomial analysis methods .

本文基于切比雪夫正交多项式数值逼近方法，提出预测智能控制算法。

The predictive intelligent control scheme is proposed , which is based on approximation theory and numerical method of Chcbyshev orthogonal polynomial .