ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS

Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.

Estimated Bounds for Zeros of Polynomials from Traces of Graeffe Matrices

In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.

APPROXIMATION PROPERTIES OF LAGRANGE INTERPOLATION POLYNOMIAL BASED ON THE ZEROS OF (1-x^2)cosnarccosx

We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.

基于正则模糊划分的模糊系统及其逼近性质

文中讨论了带有不同模糊基函数的模糊系统的逼近问题。首先,基于一维正则模糊划分和重叠函数建立多维正则模糊划分,以划分中的元素为模糊基函数设计模糊系统,应用Weierstrass逼近定理证明了该模糊系统是通用逼近器,给出了模糊系统的逼近误差界。其次,提出了多项式型、指数型和对数型模糊系统,并给出了带有隶属函数参数的逼近误差界。最后,通过数值实验对不同模糊系统的逼近能力进行了比较,实验结果进一步验证了理论分析的正确性。

一种最优化的轨迹数据L_(∞)-PLA压缩算法

随着全球定位系统的发展和应用,巨量的轨迹数据被实时收集,给数据的传输、存储和分析带来挑战.基于分段线性近似(piecewise linear approximation,PLA)的数据压缩技术因具有简单直观、压缩存储低和传输快的特点被广泛应用和研究.针对现有轨迹PLA压缩方法不能最优化地在线压缩多维数据的现状,在最大误差限定(maximum error bound,记为L_(∞))下提出多维轨迹数据的最优化PLA压缩问题(记为m DisPLA_(∞)),并给出一种在线MDisPLA算法予以解决.该算法利用“分治-融合”的策略扩展一维最优化PLA算法,以最优化地压缩多维轨迹数据.MDisPLA算法具有线性时间复杂性,可以生成最少的不连续分割,且可以保证生成直线表示的质量,即原始数据点和对应解压缩点之间的同步误差具有上界.通过与基于同步距离锥交(cone intersection using the synchronous Euclidean distance,CISED)的轨迹压缩算法进行理论和实验比较,验证了MDisPLA算法是稳健的,可生成具有保质性的直线表示.MDisPLA算法以更低的内存消耗,较CISED算法提高了14倍左右的处理速度,降低了约48%的分割个数和10.5%的存储个数.MDisPLA算法在保证压缩质量的同时,显著提高了处理速度和降低了存储空间,整体上优于CISED算法.

逼近误差有界的相容性高阶网格生成

文中提出了一种构造逼近误差有界的高质量相容性高阶网格的方法。给定两个定向的、拓扑同构的三角形网格和一组稀疏的对应点,此方法包含两个步骤:(1)生成满足误差有界的相容性高阶网格;(2)在确保逼近误差总是有界的前提下,降低网格的几何复杂度,并在该过程中通过优化控制顶点来降低相容性网格之间的扭曲以及与原始网格之间的几何近似误差。第一步先生成满足误差有界的相容性线性网格,然后升阶为高阶网格。第二步通过迭代地执行基于边长的重新网格化和增加相容性目标边长场,有效地降低了网格几何复杂度。从切空间的角度,推导出了3DBézier三角形之间映射的雅可比矩阵,从而可以有效地优化扭曲能量。通过对扭曲能量和几何近似误差能量的优化,有效地降低了相容性网格之间的扭曲以及相容性网格与原始网格之间的几何近似误差。通过大量实验,证明了此方法对于构造误差有界的高质量相容性高阶网格的有效性和实用性。

Asymptotic Approximations of Jacobi Polynomials and Their Zeros with Error Bounds

Many fields require the zeros of orthogonal polynomials. In this paper, the middle variable was improved to give a new asymptotic approximation, with error bounds, for the Jacobi polynomials P (α,β) n(cosθ) (0≤θ≤π/2,α,β>-1), as n→+∞. An accurate approximation with error bounds is also constructed for the zero θ n,s of P (α,β) n(cosθ)(α≥0,β>-1).

Asymptotic Approximations of Jacobi Functions and Their Zeros with Error Bounds

The study of zeros of orthogonal functions is an important topic. In this paper, by improving the middle variable x（t）, we＇ve got a new form of asymptotic approximation, completed with error bounds, it is constructed for the Jacobi functions φu^（α,β）（t）（α 〉 -1） as μ→∞. Besides, an accurate approximation with error bounds is also constructed correspondingly for the zeros tμ,s of φu^（α,β）（t）（α≥ 0） as μ→∞, uniformly with respect to s = 1, 2,....

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD fows

The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics(MHD)flows.The time derivative is expressed by means of Caputo’s fractional derivative concept,while the model is solved via the full-spectral method(FSM)and the semi-spectral scheme(SSS).The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques.The SSS is developed by discretizing the time variable,and the space domain is collocated by using equal points.A detailed comparative analysis is made through graphs for various parameters and tables with existing literature.The contour graphs are made to show the behaviors of the velocity and magnetic fields.The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows,and the concept may be extended for variable order models arising in MHD flows.

基于q-Bessel多项式求柯西奇异积分方程数值解

提出了基于q-Bessel多项式的离散配置法,并求解柯西奇异积分方程.首先基于q-Bessel多项式对柯西奇异积分方程中未知函数进行逼近,利用平滑变换消除积分项的奇异性.然后将积分方程转换成带有Gaussian-Legendre配置点的代数方程组,并转化成矩阵形式对其进行求解.同时给出了该方法的误差界.最后通过与文献中的其他方法进行比较,验证了该方法的可行性和有效性.

Average Error Bounds of Trigonometric Approximation on Periodic Wiener Spaces

In this paper, we study the approximation of identity operator and the convolution inte- gral operator Bm by Fourier partial sum operators, Fejer operators, Vallee--Poussin operators, Ces^ro operators and Abel mean operators, respectively, on the periodic Wiener space （C1 （R）, W°） and obtaia the average error estimations.

Error Bounds of Two Smoothing Approximations for Semi-infinite Minimax Problems

In the paper we investigate smoothing method for solving semi-infinite minimax problems. Not like most of the literature in semi-infinite minimax problems which are concerned with the continuous time version（i.e., the one dimensional semi-infinite minimax problems）, the primary focus of this paper is on multi- dimensional semi-infinite minimax problems. The global error bounds of two smoothing approximations for the objective function are given and compared. It is proved that the smoothing approximation given in this paper can provide a better error bound than the existing one in literature.

Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

In this paper we consider(hierarchical,Lagrange)reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries.We review the essential ingredients:i)a Galerkin projection onto a lowdimensional space associated with a smooth“parametric manifold”in order to get a dimension reduction;ii)an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence;iii)an a posteriori error estimation procedure:rigorous and sharp bounds for the linearfunctional outputs of interest and over the potential solution or related quantities of interest like velocity and/or pressure;iv)an Offline-Online computational decomposition strategies to achieve a minimum marginal computational cost for high performance in the real-time and many-query(e.g.,design and optimization)contexts.We present three illustrative results for inviscid potential flows in parametrized geometries representing a Venturi channel,a circular bend and an added mass problem.

插值多项式对函数|x|~α的逼近

研究插值多项式对|x|α达到最佳逼近度的一种构造方法,证明了当n=2m,m∈N,α∈(0,1]时,Fn(α)<2231-αnα,其中F2m(α)=max-1≤x≤1||x|α-R2m(x)|,R2m(x)是以x0=0,xj=cosj-12π2m(j=1,2,…,2m)为插值结点的对|x|α的Lagrange插值多项式,从而推广了M.Revers的结论.

基于多项式最小二乘算法的剔粗差研究

在飞行试验数据粗大误差处理研究中,在野值处理的算法中,采用多项式最小二乘曲线拟合算法,得到数据噪声误差方差的统计特性,以拉依尔准则为依据,首次提出使用判别野值的动态门限,来判定出野值点,并予以剔除,然后按统计特性进行补值处理,反复处理,直至野值处理完。消除各类各组飞行试验数据粗大误差,得到无粗差的飞行试验数据结果。

大型聚乙烯工业装置质量指标的次优强跟踪滤波估计

针对大型聚乙烯工业装置质量指标实时估计的复杂性,基于乙烯聚合原理推导了大型聚乙烯工业装置质量指标实时预测模型,提出了一种次优强跟踪滤波器设计方法用于根据实验室分析数据反馈修正模型预测并实时估计质量指标。所提方法在大型聚乙烯工业装置上的应用结果证实了其有效性和可行性,为实现大型聚乙烯工业装置先进控制奠定了基础。

陶瓷球轴承接触角和预紧力对高速磨削电主轴静刚度的影响

陶瓷球轴承作为电主轴的核心部件,其结构参数对电主轴的静刚度有着重要的影响。基于角接触球轴承径向刚度计算公式,通过仿真分析研究了接触角和预紧力对电主轴静刚度的影响。通过建立的主轴-轴承系统三维有限元模型,仿真获得了不同接触角和预紧力下主轴前端径向变形及主轴静刚度,进而根据有限元仿真结果拟合得到了主轴静刚度关于接触角和预紧力的拟合方程及拟合曲线。

基于拐点分割的Bezier曲线降阶

在Bezier曲线的降阶过程中,要求降阶逼近曲线与被逼曲线的误差满足容许误差条件,当不能满足给定的容许误差时,需要对被逼曲线作分割后再对各段进行降阶逼近.在现行的分割方法中,常常取中点作为其分割点,执行效率较高,但有时还是不能达到容许误差要求,这就需要再次分割.在充分考虑曲线的整体性质和光顺等条件后,提出把中点分割和拐点分割相混合的曲线降阶方式,使逼近曲线既满足一定的精度要求,又有较高的效率,利用尽可能少的分段,满足各段曲线相对光顺.实例分析表明,该方法可以获得较好的Bezier曲线的降阶效果.

球域Bézier曲线的边界

针对几何造型和产品测量中的有效误差分析和误差控制,提出了球域Bézier曲线.借助于微分几何中空间曲面族的包络算法和变量替换方法,求得球域Bézier曲线的精确边界表示;进一步利用函数逼近论中Legendre多项式的最佳一致平方逼近方法,把球域Bézier曲线的边界曲面近似地表示为一张Bézier曲面或分片Bézier曲面的组合.利用球面族的隐式方程,得到球域Bézier曲线的边界曲面的隐式方程,进而把边界曲面参数化为显式方程.理论推导和实例运算结果表明,球域Bézier曲线是一种表达方式简洁、存储空间节省、运算速度较快的误差分析和误差控制工具.

机动目标状态估计的最小均方误差界

基于多项式模型的各种自适应滤波算法被广泛应用于机动目标跟踪领域,但尚没有统一的评估标准来衡量这些跟踪算法的优劣。由于存在确定的时变未知输入,机动目标的状态估计实际为有偏估计。基于状态估计均方误差最小的准则,推导了多项式模型滤波的最小均方误差界计算方法,获得了使状态估计均方误差最小的过程噪声方差变化规律。该方法给出了各种基于多项式模型的机动目标跟踪算法的估计均方误差下限,也为机动目标跟踪中最优过程噪声方差的设定提供了依据。仿真结果验证了算法的有效性。