Copositive approximation by rational functions with prescribed numerator degree

The paper proves that, if f（x） ∈ L^p[-1,1],1≤p〈∞ ,changes sign I times in （-1, 1）,then there exists a real rational function r（x） ∈ Rn^（2μ-1）l which is eopositive with f（x）, such that the following Jackson type estimate ｜｜f-r｜｜p≤Cδl^2μωφ（f,1/n）p holds, where μ is a natural number ≥3/2＋1/p, and Cδ is a positive constant depending only on δ.

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.

APPROXIMATION BY FABER-LAURENT RATIONAL FUNCTIONS IN THE MEAN OF FUNCTIONS OF CLASS LP(T) WITH 1

Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabcrpolynomial F k,p (z),the kth p-Faber principle part F k.p (1/z) for Γ , and defined the nth p-Fcber- Laurent rational function Rn.p (f, z) and p- generalized modulus of continuity Ωp(f, t) of a function f of Lp(Γ) We inves-tigate some properties of Fk,p (z) and Fk.p (1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ω (. , t) in the mean of functions of Lp(Γ) by the rational junctions Rn.p (. . z).

Approximation Properties of Newman Type Interpolation Rational Functions with Fewer Nodes

In the present note,we consider the problem:how many interpolation nodes can be deleted from the Newman-type rational function such that the convergence rate still achieve.

RATIONAL FUNCTIONS OF BEST UNIFORM APPROXIMATION AND HOLOMORPHIC CONTINUATION OF FUNCTIONS

Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.

Muntz Rational Approximation for Special Function Classes in Orlicz Spaces

Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.

MNTZ RATIONAL APPROXIMATION FOR SPECIAL FUNCTION CLASSES IN Ba[0,1] SPACES

In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.

Neural networks for optimal approximation of continuous functions in R^d

Using some regular matrices we present a method to express any multivariate algebraic polynomial of total order n in a normal form. Consequently, we prove constructively that, to approximate continuous target functions defined on some compact set of Rd, neural networks are at least as good as algebraic polynomials.

Optimization for ASP flooding based on adaptive rationalized Haar function approximation

This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer(ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method,the experimental comparison method and control vector parameterization(CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.

A Rational Approximation of the Fourier Transform by Integration with Exponential Decay Multiplier

Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from the shifting property of the Fourier transform. In this work, we show how to represent the Fourier transform of a function f(t) in form of a ratio of two polynomials without any trigonometric multiplier. A MATLAB code showing algorithmic implementation of the proposed method for rational approximation of the Fourier transform is presented.

APPROXIMATION RATES OF ERROR DISTRIBUTION OF DOUBLE KERNEL ESTIMATES OF CONDITIONAL DENSITY

In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .

半无限介质多自由度频响函数离散时间有理近似的稳定参数识别

离散时间有理近似函数是将半无限土频响函数转化为时域模型的重要工具,离散时间有理近似函数和时域模型具有相同的稳定性和精度。目前关于离散时间有理近似函数的研究只针对于单自由度系统。该文基于线性控制理论,给出了多自由度有理近似系统的稳定条件。将稳定性条件与遗传-序列二次算法相结合,开发了多自由度频响函数参数辨识方法,保证了多自由度系统的稳定性和精度。不同维度的多自由度有理近似系统的数值仿真验证了该文方法可以保证多自由度有理近似系统的稳定性和精度。

基于Kriging模型及变异函数的批次产品免调率提升方法研究

平衡力式密封电磁继电器在装配完成后的性能测试中合格率相对较低,需要大量的调试来使产品合格率提升。针对吸合释放电压的计算,通过灵敏度分析确定4个关键输入参数,均与永磁体相关;基于最优拉丁超立方抽样方法选择输入参数的样本点,建立电磁系统有限元模型;根据静态特性数据建立Kriging近似模型,利用变异函数对Kriging模型进行修正以减小误差,实现吸合释放电压的快速计算;通过与有限元模型的对比,验证了快速计算模型的精度。基于所建立的快速计算模型,进行免调率参数设计和容差设计,并通过实际样机生产验证了免调率提升效果。

Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment

In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.

The essential rate of approximation for radial function manifold

In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r（B^d） be the usual Sobolev class of functions on the unit ball 54. We study the deviation from the radial function manifolds to WP^r（b^d）. Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.

应用电站设备宽频特性的过电压在线监测装置

过电压的监测和分析对现代电力供电系统有极其重要的意义。通过分析比较国内外现有过电压在线监测装置的特点,提出了一种新型的利用设备宽频传输特性的过电压在线监测方法,其原理是将电压互感器(TV)、二次电缆和分压器等二次设备看作相互级联的二端口网络,通过有理函数逼近建立了其传输参数模型;基于该模型,可由二次设备输出端口的电压信号,应用离散Fourier变换反演计算得到TV高压端口即高压母线上的过电压信号。同时应用该方法设计了在线监测装置的硬件结构电路,开发了软件运行程序,在实验室搭建了该过电压监测装置并建立了该装置的整体计算模型,计算结果与实测数据的比较验证了监测方法和监测装置的可行性和有效性。

频变输电线路模型中的低阶拟合方法

对特征阻抗和传播系数的有理函数拟合是考虑参数频变的输电线路建模中的关键步骤。传统的模域输电线路模型采用的Bode渐近线拟合法会产生大量零极点,其中一部分对提高模型精度没有作用并会导致电磁暂态仿真中产生不必要的计算。为避免冗余零极点的产生,提出了一种应用于频变输电线路模型中的低阶有理函数拟合方法。首先对线路特征阻抗和传播系数进行低阶零极点定位,然后用非线性最小二乘法提高拟合精度,从而实现对特征阻抗和传播系数的低阶有理函数拟合。对比Bode渐近线法的拟合结果,低阶拟合方法能够在保证拟合精度的同时降低拟合函数的阶数,从而提高电磁暂态计算效率。

Mntz有理逼近的点态估计

给定 M >0 ,设Λ ={λn} ∞n=1是一个实数序列 ,满足 0≤λ1<λ2 <… ,且对所有 n≥ 1,有λn+ 1-λn≥ Mn .本文得到了 Müntz系统 { xλn}有理逼近的一个点态估计 .

矿井瞬变电磁矩形回线源瞬变电磁响应

为研究均匀全空间介质中任意点(除发射框边)处矩形回线源瞬变电磁响应,从全空间磁偶极子的切向电场和水平圆形回线发射框中心磁场出发,采用互易原理和积分法推导了全空间任意点处的瞬变响应。通过对全空间瞬变场磁场Bz及其时间导数Bz/t的核函数Y(ω)和Y'(ω)特征的研究,将全程瞬变响应分为早期、中期和晚期。Y(ω)的早期和晚期阶段,其内层误差函数采用渐近展开式,外层积分采用直接多项式积分;中期阶段,内层误差函数采用有理契比雪夫展开式,外层积分采用龙贝格积分。Y'(ω)的晚期和非对角区域的早期采用误差函数渐近展开式;Y'(ω)的中期和对角区域的早期采用龙贝格积分。采用理论模型计算验证了公式的精度。结果表明,该算法求取的数值解,其Bz核函数Y(ω)的相对误差可以控制在1×10-6%以内;而Bz/t的核函数Y'(ω)的相对误差可以控制在1×10-4%以内。早期阶段,Bz和Bz/t在发射框内部的极值中心沿着与短边呈45°夹角方向向发射框内部移动,并且短边处的2个极值中心先行合并,然后再沿长边方向合并;相同时刻,Bz过零点等值线比Bz/t过零点等值线传播的更远。

带权Bernstein基的对偶基函数在等距逼近中的应用

利用带权Bernstein基的对偶基函数,给出了Bernstein基的对偶泛函和平方可积函数的最小二乘逼近算法,并考虑了满足端点高阶约束条件时的情形.将该算法应用于Bézier曲线等距曲线多项式逼近算法中,不仅可以获得显式的同阶Bézier逼近曲线,还可以满足端点高阶约束条件,进一步还可得到有理逼近算法.数值实例以及与其他算法的比较显示了文中算法的有效性.