The Discrete Approximation Problem for a Special Case of Hermite-Type Polynomial Interpolation

Journal of Systems Science and Complexity - Every univariate Hermite interpolation problem can be written as a pointwise limit of Lagrange interpolants. However, this property is not preserved for...     

The Fitzpatrick-Neville-Type Algorithm for Multivariate Vector-Valued Osculatory Rational Interpolation

In this paper,the authors first apply the Fitzpatrick algorithm to multivariate vectorvalued osculatory rational interpolation.Then based on the Fitzpatrick algorithm and the properties of an Hermite interpolation basis,the authors present a Fitzpatrick-Neville-type algorithm for multivariate vector-valued osculatory rational interpolation.It may be used to compute the values of multivariate vector-valued osculatory rational interpolants at some points directly without computing the interpolation function explicitly.     

Interpolation Method Research and Precision Analysis of GPS Satellite Position

According to the precise ephemeris has only provided satellite position that is discrete not any time,so propose that make use of interpolation method to calculate satellite position at any time.The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation,Newton interpolation,Hermite interpolation,Cubic spline interpolation method,Chebyshev fitting method respectively,which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst,the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore,Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.     

基于BFOA的拉格朗日插值点最优配置

拉格朗日插值法是工程中常用的函数近似重构技术,其有效性与采样点的位置选择密切相关。细菌觅食优化算法(BFOA)则是一种新兴的模拟大肠杆菌觅食行为的群体智能算法,目前尚未得到广泛的应用。提出利用细菌觅食优化算法进行拉格朗日插值点的优化求解,结果优于传统方法。本研究验证了细菌觅食优化算法的有效性,同时为拉格朗日插值点的最优配置提供了新的解决思路。     

Flow shop问题的蚁群优化调度方法

提出了一种新颖的蚁群优化算法，用于解决流水作业（flowshop）的优化调度问题。算法中，流水作业调度问题以结点或弧模式有向图表示，人工蚁受有向图上信息素踪迹的指引，在图上搜索并一步步构造出问题的可行解。算法中的信息素踪迹更新过程作为蚁群间的间接通信机制，将引导整个蚁群收敛到问题的优化解。信息素踪迹更新过程中的停滞状态脱离机制以及信息素踪迹限制机制能帮助人工蚁跳出局部最优解。算法局部搜索过程中采用的基于关键路径的领域结构缩小问题的搜索空间。与其他算法在Taillard流水作业调度测试问题集上的比较试验表明，本算法性能更优，且具有更强的自适应和鲁棒性。     

On the unique minimal monomial basis of Birkhoff interpolation problem

This paper studies the minimal monomial basis of the n-variable Birkhoff interpolation problem. First, the authors give a fast B-Lex algorithm which has an explicit geometric interpretation to compute the minimal monomial interpolation basis under lexicographic order and the algorithm is in fact a generalization of lex game algorithm. In practice, people usually desire the lowest degree interpolation polynomial, so the interpolation problems need to be solved under, for example, graded monomial order instead of lexicographic order. However, there barely exist fast algorithms for the nonlexicographic order problem. Hence, the authors in addition provide a criterion to determine whether an n-variable Birkhoff interpolation problem has unique minimal monomial basis, which means it owns the same minimal monomial basis w.r.t. arbitrary monomial order. Thus, for problems in this case, the authors can easily get the minimal monomial basis with little computation cost w.r.t. arbitrary monomial order by using our fast B-Lex algorithm.     

基于峭度的稳健特定信号盲提取

在盲源提取中,当所要提取信号的峭度在某一区间时,可以采用基于峭度的方法将期望的信号提取出来。如果采用外点惩罚函数法来求解,理论上要求惩罚因子趋于无穷大时才可能收敛到最优解,但是惩罚因子的增大往往导致代价函数的Hessian矩阵病态化。因此,这种方法在实际中稳健性很差。提出了采用Lagrange乘子法来解决特定信号的提取问题,与采用外点惩罚函数法的算法相比,这种方法在惩罚因子相对较小的情况下也能得到最优解。计算机仿真和实际的胎儿心电试验表明了这种方法在收敛速度和稳健性上要优于采用外点惩罚函数法的算法。     

一种渐进式平滑轨迹线标绘方法

为实现GIS系统和分布式仿真中运动轨迹线的绘制,提出一种基于Catmull曲线算法的渐进式标绘方法。本方法可根据定位点获得具有连续平滑性质的轨迹线,并随定位点的增加实现轨迹线延伸,延伸的轨迹线可与原轨迹线保持连续平滑性;通过曲线离散化参数调整轨迹线的平滑度;通过依赖于轨迹线的线性插值获取任意时刻的位置信息。实验结果表明,轨迹线标绘方法可以实现基于定位点的渐进式平滑标绘,添加一个定位点的计算时间可在0.1ms内完成。     

Resultant elimination via implicit equation interpolation

It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.     

一种新的连续特征量化方法

对连续特征进行有效量化是水下目标分类中有待解决的一个重要问题。本文提出一种加权距离量化方法。该量化方法使用类别相对频率构造了两相邻区间的加权距离,将加权距离作为特征量化标准,在量化过程中,将加权距离最小的相邻区间进行合并,直到满足终止条件为止。文中使用递归最小信息熵、Chi2、加权距离等五种量化算法对27维水下目标的识别特征进行了量化处理,比较了各量化方法的性能。结果表明,使用加权距离量化算法对水下目标的识别特征进行量化处理之后,所产生的量化区间数目较少,量化时间较短,量化数据较好的保持了原数据的分类能力,且量化数据的分类时间也大大缩短。     

贝叶斯网络参数学习中的连续变量离散化方法

首先从离散方案对推理功能的影响出发,提出将条件信息熵作为评判离散方案好坏的标准;其次从降低问题求解的复杂度出发,提出将贝叶斯网络划分为多个极小简单子网分别进行离散化;最后,依据离散化问题与路径规划问题的相似性,设计了一套利用蚁群算法进行问题求解的方法。实验表明,采用所提方法进行贝叶斯网络连续变量离散化,能很好地将连续变量的取值空间进行分类,从而达到良好的推理效果。     

An Improved Early Termination Sparse Interpolation Algorithm for Multivariate Polynomials

This paper presents an improved early termination algorithm for sparse black box multivariate polynomials, which reduces the interpolation problem into several sub-interpolation problems with less variables and fewer terms. Actually, all interpolations are eventually reduced to the interpolation of a list of polynomials with less terms than that of the original polynomial. Extensive experiments show that the new algorithm is much faster than the original algorithm.     

基于环节的控制系统图形组态仿真软件

介绍了一个基于环节的控制系统图形组态仿真软件的功能和实现方法，及改进的仿真算法，在数值计算方法中，引入了拉各朗日线性插值方法，既大大减少了迭代计算量，又保持了原有的仿真精度，利用这一可视化仿真平台，用户可对线性系统，多变量系统，多变量Smith预估控制系统，采样系统等方便快捷地建立方框图形式的系统仿真模型，从而为复杂系统的分析和设计提供了仿真研究平台，系统界面友好，易于扩展。     

约束最小二乘无源定位算法的求解与分析

针对约束最小二乘无源定位算法中最优Lagrange乘数的求解问题,提出了新的计算方法。通过详细分析该定位算法的最优化问题求解过程,给出了求解最优Lagrange乘数的准确公式,同时将其转化为等价的多项式方程,并推导了相应的多项式方程系数。通过仿真实验,分析了最小二乘定位算法的性能,重点分析了最优Lagrange乘数的选取对算法性能的影响,并给出了经验选取方法,验证了所提方法的正确性和有效性。     

超高速撞击仿真算法分析

分别用拉格朗日(Lagrange)算法、欧拉(Euler)算法及光滑粒子流体动力学(SPH)算法对超高速撞击问题进行了数值仿真,对各种算法的优劣性进行讨论及对比研究。与传统的拉格朗日算法欧拉算法相比,新兴的SPH算法更适宜于超高速撞击仿真分析。     

LFM信号参数估计的插值FRFT算法

提出了一种基于分数阶傅里叶变换（fractional Fourier transform, FRFT）的线性调频（linear frequency modulation, LFM）信号参数估计的插值算法。首先针对FRFT的旋转角度α搜索步长问题,提出了在较大搜索步长下进行插值以得到α精估计的方法;然后针对离散分数阶傅里叶变换(digital fractional Fourier transform, DFRFT)因参数u离散化而造成的栏栅效应问题,采用相邻谱线进行插值以得到u的精估计;最后用α和u插值精估计结果对单分量LFM信号的参数进行估计。这一方法在不影响估计精度的前提下,降低了计算量和复杂度。仿真结果表明,在较低的信噪比下,LFM信号参数估计的精度仍十分逼近克拉美罗界(Cramer-Rao bound, CRB)。     

Troubleshooting algorithm for solving assignment problem and its applications

A new troubleshooting algorithm for solving assignment problem based on existing algorithms is proposed, and an analysis on the related theory is given. By applying the new troubleshooting algorithm to the Lagrange relaxation algorithm of the multi-dimensional assignment problem of data association for multi-passive-sensor multi-target location systems, and comparing the simulation results with that of the Hungarian algorithm which is the classical optimal solving algorithm, and the multi-layer ordersearching algorithm which is a sub-optimal solving algorithm, the performance and applying conditions of the new algorithm are summarized. Theory analysis and simulation results prove the effectiveness and superiority of the new algorithm.     

Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error

In this paper, two new interpolation algorithms lot CNC machining along curve~l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds ＇~under＂ the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.     

压缩感知视角的鲁棒波达角估计算法

从压缩感知的视角对鲁棒波达角估计进行了探索,通过将可能存在的波达角进行空间离散化,从而将波达角估计问题转换为压缩感知信号支撑恢复问题。同时将阵元存在的增益失配、相位失配和阵元间互耦等非理想因素,通过一阶近似,将其建模成均值为理想流形矩阵的随机矩阵,从而建模了阵列非理想特性和波达角空间离散化带来的误差。基于这种新的随机测量矩阵模型,提出了一种基于压缩感知的鲁棒波达角估计算法,分析表明本文提出算法对阵列模型扰动和角度空间离散化具有良好的鲁棒性。仿真验证了分析结果。     

Regression Function Comparison for Paired Data

In this paper, the regression function comparison for paired data is studied. The proposed test statistic is based on the weighted integral of characteristic function marked by the difference of responses. There are several merits of the proposed statistic. For instance, it takes a simple V-statistic form. No bandwidth is needed. No moment conditions are required for covariates. It can be applied to covariates of any fixed dimension. The asymptotic results are also developed. It is proven that n times the proposed test statistic converges to a finite limit under the null hypothesis and the test is consistent against any fixed alternatives. Local alternative hypotheses which converge to the null hypothesis at the rate of n-1/2 are also detected. A suitable Bootstrap algorithm is also proposed for the implementation of the proposed test statistic. Simulation studies are carried out to illustrate the merits of the proposed method. A real data example is also used to illustrate the proposed testing procedures.