The method of calculating the perturbed Chebyshev-Padé approximation is proposed for not only the general situation but also some special cases, i. e., an odd function and an even one.
提出了一种新的带有扰动的Chebyshev-Padé逼近，它依赖于一个扰动参数，其优点在于：它可以通过调整扰动参数来提高逼近的精度。
The Chebyshev polynomial approximation is used to investigate the stochastic bifurcation of van der Pol system with two-sided barriers.
利用随机光滑动力系统的Chebyshev正交多项式逼近方法，研究了双边约束条件下随机van der Pol系统的分岔现象。
Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.
首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。
It is shown that the Chebyshev polynomial approximation is a valid method for the investigation of non-smooth systems.
研究表明，Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法。
Based on this thought, in this thesis, the alternation theorem is first extended to the Chebyshev approximation problems with inequality constraints, and then two algorithms are devised for designing linear phase FIR filters with inequality constraints in Chebyshev sense according to the extended theorem.
L.J.Karam和McClellan在文献[20]中把交错点组定理扩展到复数域，并提出了求解复系数FIR滤波器的复Remez算法，但由于此扩展定理只是一个充分条件，所以此算法不能保证得到最优解。在文献[23]中，他们对复Remez算法进行了完善，使其收敛到最优解。
Studying the best mixed-norm approximation for nonlinear cases, this paper gives characterizations of such approximation for a family of not mere convex subsets, which includes Kolmogorov's type theorem and Chebyshev alternation theorem, etc.
本文研究了非线性最佳混合范数逼近问题，对一类不仅仅是凸的子集给出了最佳混合范数逼近的特征，其中包括了Kolmogorov型定理和Chcbyshcv交错定理等。
A theorem on estimate of pointwise approximation of bounded variation functions defined on by the partial sums of the second Chebyshev-Fourier series is obtained, and this theorem to monotonic type continuous functions is applied.
得到了第二类Chebyshev-Fourier级数部分和对[-1,1]上有界变差函数点态逼近估计的一个定理，并把这个定理应用于单调型连续函数。
Chebyshev polynomial approximation is applied to the period-doubling bifurcation problem of a stochastic van der Pol system with bounded random parameters and subjected to harmonic excitations.
应用Chebyshev多项式逼近法研究了谐和激励作用下具有随机参数的随机vanderpol系统的倍周期分岔现象。
Period-doubling bifurcation analysis of stochastic van der Pol system via Chebyshev polynomial approximation
基于Chebyshev多项式逼近的随机vanderpol系统的倍周期分岔分析
The main works as follows: Firstly, stochastic van der Pol system with random parameter subject to an arch-like probability density function is reduced into its equivalent deterministic one using Chebyshev polynomial approximation method.
应用Chebyshev多项式逼近法把含有服从拱形分布随机变量的vanderpol系统转化为等价确定性扩阶系统，再利用一般数值方法研究了该系统的对称破裂分岔和倍周期分岔行为。
Numerical simulations show that similar to their counterpart in deterministic nonlinear system some symmetry-breaking bifurcation may occur in the stochastic Duffing-Van der pol system, and Chebyshev polynomial approximation is an effective approach in solving dynamical problems of nonlinear system with random parameter.
数值模拟显示随机Duffing-vanderpol系统与确定性均值参数系统有着类似的对称破裂分岔行为，文中的主要数值结果表明Chebyshev多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法。
The Chebyshev polynomial approximation was applied to the dynamical response problem of the stochastic Duffing-van der Pol system with random parameters. First, the stochastic Duffing-van der Pol system was reduced into an equivalent deterministic one for substitution.
对一类含随机参数的Duffing-vanderpol系统，运用Chebyshev多项式逼近法，将其转化成等价的确定性扩阶系统；
Numerical results for the original stochastic Duffing-van der Pol system obtained separately by the Mento-Carlo method and the Chebyshev polynomial approximation are compared to show the effectiveness and efficiency of the latter method in solving the nonlinear dynamical problems of system with bounded random parameters.
数值模拟结果显示，Chebyshev正交多项式逼近法是研究含有界随机参数的耦合非线性动力学系统的一种有效方法。
A new application of genetic algorithm in FIR filter with weighting Chebyshev optimal approximation method is presented.
介绍了一种遗传算法在FIR数字滤波器设计&加权切比雪夫最佳逼近准则优化设计方法中的应用。
The Application of Chebyshev Polynomial Approximation in Geodetic Calculation
切比雪夫多项式逼近在大地测量计算中的应用
In this paper, for the function of Chebyshev expansion, the approximating function having the approximant's order of Chebyshev polynomials is given by means of Faber mapping and quadratic Pad é approximation of power series, and it is also expressed by the fraction of Chebyshev polynomials.
对于具有Chebyshev展式的函数，文章利用Faber映射及幂级数二次Padé逼近，给出其具有关于Chebyshev正交多项式的逼近阶的逼近函数，并将其用Chebyshev正交多项式分式表示。
Based on the approximation theory, this paper presents a new neural network model based on Chebyshev orthogonal multinomial.
基于逼近论，将一组Chebyshev正交多项式取代BP网络中的S型函数，构成一种新的神经网络模型。
By using MATLAB signal and using window method, frequency sampling and Chebyshev approximation the design of low pass digital filter in the toolbox have been processed.
采用窗函数法、频率抽样法和切比雪夫最佳一致逼近法，通过调用Matlab信号处理工具箱中的函数设计低通数字滤波器。
It adopts Chebyshev polynomial technology which has low approximation error and fast converging speed to approach sine function of acceleration/deceleration expression, and speed and displacement are directly calculated according acceleration's quadratic polynomial to avoid the influence of approximation error on parameter calculation.
采用逼近误差小、收敛速度快的契比雪夫多项式对加速度正弦函数二阶展开，速度、加减速区间长度等参数则直接利用基于二阶多项式的加速度求解，避免了函数逼近误差对参数计算的影响。
In this paper, an optimum design method of FIR DF based on equivalent ripple Chebyshev approximation rule is introduced. It was proved to be an optimum design method by simulation implementing based on MATLAB.
介绍了一种基于等波纹切比雪夫逼近准则的FIR数字滤波器的最优化设计方法，通过MATLAB的仿真实现，证明了该方法是一种最优化的设计。