ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

Least-squares function-valued Padé-type approximation and its application in solving integral equations

To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function： valued Pad＆type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Padetype approximation is given. In the end, an example is given to show that the method is effective and stable.

Degeneracy Cases of Generalized Inverse Function-Valued Padé Approximation

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application.

PADE APPROXIMANTS AS LIMITS OF RATIONAL FUNCTIONS OF BEST APPROXIMATION IN ORLICZ SPACE

In this paper, we prove that the best rational approximation of a given analytic function in Orlicz space L~*(G), where G = {|z|≤∈}, converges to the Pade approximants of the function as the measure of G approaches zero.

CONVERGENCE IN MEASURE OF MULTIVARIATE PADE APPROXIMANTS

Convergence conclusions of Pade approximants in the univariate case can be found in various papers. However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergence for multivariate Pade approximants,she gives in[2]a de Montessus de Bollore type theorem.In this paper,we will discuss the zero set of a real multivariate polynomial,and present a convergence theorem in measure of multivariate Pade approximant.The proof technique used in this paper is quite different from that used in the univariate case.

Adomian decomposition method and Padé approximants for solving the Blaszak-Marciniak lattice

The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.

Adomian Decomposition Method and Padé Approximants for Nonlinear Differential-Difference Equations

有 Pad é approximants 的联合 Adomian 分解方法(ADM ) ，我们解决二个微分差别的方程(DDE ) ：相对论的 Toda 格子方程和修改 Volterra 格子方程。在符号的计算枫树的帮助下， ADM-Pad é技术获得的结果与独自使用 ADM 获得的那些相比。数字结果比使用 ADM 证明 ADM-Pad é技术在集中的更大的领域与更快的集中率和更高的精确性和亲戚给近似答案。

The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant

In this paper, the extended Pade approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter ~ is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.

COMPUTATION FORMULAS OF GENERALIZED INVERSE PAD APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS

For the generalized inverse function-valued Pade approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form.

THE ORTHOGONAL POLYNOMIALS AND THE PADE'APPROXIMATION

The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on [ -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used tofined the denomiators of some functions.

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

Numerical Solution of the Diffusion Equation with Restrictive Pade Approximation

The problem of solving the linear diffusion equation by a method related to the Restrictive Pade Approximation (RPA) is considered. The advantage is that it has the exact value at certain r. This method will exhibit several advantages for example highly accurate, fast and with good results, etc. The absolutely error is still very small. The obtained results are compared with the exact solution and the other methods. The numerical results are in agreement with the exact solution.

使用Pade近似式处理数字控制系统中的纯滞后

针对使用改进ｚ变换处理数字控制系统中的纯滞后，需要查表和进行繁杂的数学运算，提出在ＭＡＴＬＡＢ的环境下，使用Ｐａｄｅ近似式拟合纯滞后因子，和不带滞后的被控对象串联组合、离散化，结果有较高的精确度．仿真证明此方法的正确性与实用性．

一种基于Pade近似的频域辨识与频域模型降阶新方法

研究了基于积分最小二乘指标的SISO时滞系统频域辨识与频域模型降阶问题 .通过采用Pade近似 ,将积分最小二乘指标推广到可以处理时滞系统的情形 .深入分析了Pade近似所引入误差 ,揭示了采用Pade近似的可行性与有效性 .所提出的方法能够用最小二乘类算法高效求解 ,无须困难的非线性优化 .

类Pade逼近方法在二维非线性振动系统的应用

提出一种求解强非线性系统同异宿轨道解析解的改进类Pade逼近方法,该方法在分析带有扰动参数的系统时无需预先限定参数的取值范围.首先研究了具有三次非线性项的系统,分析其产生同宿或异宿轨道时参数的取值范围,分别提出直接体现参数的同宿及异宿解的设解通式,据此获得了一类强非线性下的自治系统方程的同宿及异宿解.其次,对于非自治系统,研究了具有三次非线性项系统的强迫振动,直接考虑扰动参数对整个系统的影响,得到了满足同(异)宿边界条件的周期解.最后,构造了两种不同形式的异宿解,从而减少了保守系统异宿解的计算量.借助数值模拟验证了该方法的有效性及精确性.

基于Taylor和Pade能逼近的滞后系统IMC-PID研究

针对一阶加纯滞后过程,对滞后项分别进行Taylor逼近、一阶Pade逼近、二阶Pade逼近和全通逼近,设计出基于内模原理的PID反馈控制器,对其参数整定进行分析,并进行仿真实验,评价了各种PID控制器的适用情况.

基于Pade近似一般形式的IMC-PID控制器设计

内模控制方法因具有诸多优点而引起了业界的广泛关注,但难以在DCS中直接实现,现有的IMC-PID设计方法存在着只针对特定模型才能设计或通用设计但近似程度偏低的问题,提出了一种新的IMC-PID控制器设计方法,采用一般形式的Pade多项式逼近IMC-PID转化过程中出现的复杂项,然后对照该Pade多项式和PID控制器表达式设计PID控制器参数。该方法广泛适用于各种单变量对象,也能够毫无修改地应用于多变量系统的IMC-PID控制器参数设计。与基于M ac laurin展式的IMC-PID设计方法相比,该方法提供了具有更强理论依据的微分滤波时间常数计算式,能够获得与内模策略更为接近的控制效果。

磁流变半主动悬架时滞的LQG-Pade逼近合拍控制

为降低时滞对磁流变半主动悬架工作效果的负面影响,提出一种有别于常规控制量预测时滞补偿的LQG-Pade逼近合拍(LQG-Pade approximation rhythmic,LQGPAR)时滞控制方法。首先,建立考虑时滞的1/4车2自由度的磁流变半主动悬架模型,并基于此模型设计LQG控制器求得理想主动力信号。其次,通过对理想主动力信号进行Pade逼近操作获取考虑时滞的滞后主动力信号,并根据该信号和悬架相对运动速度求取磁流变减振器的控制电流,进而使磁流变减振器的实际响应和悬架相对运动速度合拍。最后,以无时滞控制措施的LQG(无措施LQG)控制器、理想LQG控制器(无时滞)、史密斯预估-LQG(Smith Predictor-LQG,SPLQG)时滞补偿控制器及被动悬架为比较对象,进行悬架性能对比与分析。结果显示:时滞对悬架系统高频振动影响比较明显,尤其是对振动能量集中在高频段内的车轮动载荷的影响最为明显,时滞越大,悬架系统高频振动的抑制效果越差,其中无措施LQG控制器所受影响最为明显;与被动悬架相比,时滞分别为25ms和30ms时,SPLQG控制器能使悬架综合性能分别改善18.69%和8.75%,而LQGPAR控制器可使悬架综合性能分别改善32.24%及29.28%。

迟后时滞系统Pade等效式的最佳阶次分析研究

时滞现象是生产过程中常见的现象,是影响系统稳定性的一个重要因素;因此研究时滞环节对于解决工程中的时延问题,提高控制系统性能有着重要意义。现建立一种求延时环节的对称Pade展开式最佳等效阶次的简便方法。首先,阐述了开环传递函数中的最小相位环节和延时常数部分,对延时环节最佳Pade等效阶次的影响;其次,建立相对均方根误差指标,分析了Pade等效阶次、延时时间参数及Pade展开式中极点与虚轴的距离三者之间的关系,并确定控制系统中延时环节的Pade等效最佳阶次的方法;最后,验证了求Pade最佳等效阶次方法的准确性,表明该方法能快速有效地求出延时环节的Pade等效的最佳等效阶次。

基于Pade逼近的Cole-Cole频散介质GPR有限元正演

针对Cole-Cole频散介质中的复介电常数是jω的分数次幂函数,传统的时域有限元法难以离散及计算时间域分数阶导数,本文采用Pade逼近算法将含有时间分数阶导数的Cole-Cole频散介质电磁波方程推导为一组整数阶辅助微分方程,提出了一种适用于Cole-Cole频散介质的GPR有限元正演模拟算法.在复数伸展坐标系下,通过在频率域Cole-Cole频散介质电磁波方程中引入2个中间变量,并将其变换到时间域,从而以变分形式将PML边界条件加载到Cole-Cole频散介质GPR有限元方程组中,并给出了详细的求解公式.在此基础上,编制了基于Pade逼近的Cole-Cole频散介质GPR有限元正演程序,利用该程序对均匀模型进行计算,并与解析解进行对比,验证了本文构建的GPR有限元正演算法的正确性和有效性.设计了一个复杂Cole-Cole频散介质GPR模型,利用本文构建的GPR有限元正演算法进行模拟并与非频散介质模型的模拟结果进行对比,分析了电磁波在Cole-Cole频散介质中传播衰减增强、子波延伸,分辨率降低等传播规律,有助于实测雷达资料更可靠、更准确的解释.模拟结果表明,基于Pade逼近的GPR有限元正演算法可用于复杂Cole-Cole频散介质结构模拟,且具有较高的计算精度.