基于多项式模型的OFDM信道盲估计

采用二元多项式模型对时变OFDM系统的时频响应进行建模.在多项式模型的基础上,结合期望最大化(EM)方法的思想,提出了一种利用时频面上的二维数据来获取模型参数的最大似然(ML)估计值的算法(PEMTO).为了降低计算复杂度,避免由于矩阵求逆而带来的风险,给出了PEMTO的一种迭代计算方法(RPEMTO)PEMTO算法在数学上进行简化后,可以用来进行一维序贯信道估计.仿真结果显示,所提出算法的误码率低于其他类型的盲估计算法.     

矩阵最小多项式的求解及应用

综述了三种求矩阵最小多项式的算法,同时讨论了矩阵最小多项式的一些性质,并举例说明了矩阵最小多项式在代数问题、常系数微分方程组求解上的应用．     

特征多项式与最小多项式相等的充要条件及其应用

给出了矩阵的特征多项式与最小多项式相等的几个充分必要条件以及它们的应用.     

Conversion matrix between two bases of the algebraic hyperbolic space

This paper presents the matrix representation for the hyperbolic polynomial B-spline basis and the algebraic hyperbolic Bézier basis in a recursive way, which are both generated over the space Θ_n = span {sinht, cosht, t^n?3, …, t, 1} in which n is an arbitrary integer larger than or equal to 3. The conversion matrix from the hyperbolic polynomial B-spline basis of arbitrary order to the algebraic hyperbolic Bézier basis of the same order is also given by a recursive approach. As examples, the specific expressions of the matrix representation for the hyperbolic polynomial B-spline basis of order 4 and the algebraic hyperbolic Bézier basis of order 4 are given, and we also construct the conversion matrix between the two bases of order 4 by the method proposed in the paper. The results in this paper are useful for the evaluation and conversion of the curves and surfaces constructed by the two bases.     

关于Sylvester与Frobenius不等式等号条件的研究

应用新近得到的矩阵多项式秩的恒等式,对矩阵秩的Sylvester不等式和Frobenius不等式限定在矩阵多项式上取等号的条件进行进一步讨论,同时给出近期相关结果的一种统一的证明方法。     

Time Collocation Method for Structural Dynamic Problems

In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving alge-braic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients, which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.     

完全二部图的图多项式及图的不同特征根个数的下界

本文首先圆满解决了完全二部图的图多项式问题;然后讨论了只有平凡多项式图的一类图的共同性质;最后利用图多项式给出了图G的不同特征根个数的新下界。     

Abhyankar反演公式的解析证明

以证明Jacobi猜想为重要目的,求出多项式映射的逆映射的具体形式,即Abhyankar反演公式,给出了求解多项式映射的逆的一个新思路.不同于该公式由Abhyankar以组合数学的方式给出的原证明,本文采用解析的方法给出了Abhyankar反演公式在二维情况下的一个新的证明.     

四元数矩阵的带状多项式

利用相似这个概念对实矩阵变元的带状多项式进行了合理的推广，给出了四元数矩阵变元的带状多项式的定义，并且证明了其相应的一些性质，这些性质在四元数多元统计分析中，已经成为推导非中心分布的必需的工具。     

Lucas多项式的性质

本文在研究Fibonacci多项项若干性质的基础上，给出了Lucas多项式Ln（x）的定义及其有关性质。     

Control synthesis for polynomial nonlinear systems and application in attitude control

A method for positive polynomial validation based on polynomial decomposition is proposed to deal with control synthesis problems. Detailed algorithms for decomposition are given which mainly consider how to convert coefficients of a polynomial to a matrix with free variables. Then, the positivity of a polynomial is checked by the decomposed matrix with semidefinite programming solvers. A nonlinear control law is presented for single input polynomial systems based on the Lyapunov stability theorem. The control synthesis method is advanced to multi-input systems further. An application in attitude control is finally presented. The proposed control law achieves effective performance as illustrated by the numerical example.     

第二类Fredholm积分方程的快速数值解法

对于具有弱奇性核函数的第二类Fredholm积分方程，将核函数所定义的区域分成大小不同的正方形子区域，利用分层插值多项式逼近核函数，由此得到近似矩阵B实现了积分方程的快速数值解法。在最后，对如何提高方案的数值稳定性作简要讨论并给出要讨论并给出数值结果。     

用程序解加权最小二乘拟合多项式的系数

本文首先简单介绍了最小二乘法原理和利用加权最小二乘法求拟合多项式的系数问题,然后利用C语言设计求解加权最小二乘拟合多项式系数的程序．只要输入给定的数据点、相应的权重和所求拟合多项式的次数,运行该程序后就能准确地、高精度地得到拟合多项式的系数．     

关于Q上不可约多项式的一个注记

指出文献「１」中的一个错误结论。并进一步讨论了一元多项式在有理数范围内的不可约性，给出了一个多项式的根全是实数的一个必要条件。     

MIMO OFDM系统中基于多项式求根的频偏估计算法

基于频域训练序列,深入地分析了MIMO—OFDM系统中基于多项式建模的频偏估计问题．设计训练序列使其结构满足适当的条件,根据相应矩阵的厄尔密特属性和实对称属性,分析出代价函数多项式方程根的成对性,进而提出整数频偏与小数频偏可同时通过直接多项式求根方法估计出来．分析了导数多项式求根方法与直接多项式求根方法,研究出代价函数多项式与其导数多项式具有公共的多项式因子,且代价函数多项式可以表示成该公共多项式因子的二次型,并进一步揭示出二者在估计上的等效性以及后者在实现上的优越性．计算机仿真结果验证了该理论分析结果．     

Taylor’s polynomial and infinitesimals

Taylor’s theorem in analysis provides a way of approximating an n+1-times differentiable real function by an nth degree polynomial in a neighbourhood of a point x ₀. The usefulness of the theorem lies in the fact that if the bounds on |f ⁽ⁿ⁺¹⁾(x)| are known, then the error introduced by the polynomial approximation can be estimated. So while Taylor’s theorem provides an extremely useful manner of approximating the given function to a desired degree of precision in a neighbourhood of a given point, it says nothing about the nature of the polynomial approximation itself, and intuitive arguments are often offered to explain why the derivatives of f must figure in the coefficients of such a polynomial. In what follows, we shall attempt a rigorous explanation of the sense in which such a polynomial is the ‘best’ approximation of the given function.     

一种C^2连续的三次样条插值方法

利用Bernstein多项式构造一种C^2连续的三次样条插值。证明其存在唯一性与一致收敛性．并给出误差上界的估计．与传统算法比较。避开了求解方程组的困难．     

方形网格上的Stieltijes型混合有理插值

文章基于Stieltijes型分叉连分式有理插值,结合Thiele型连分式及Newton多项式,构造了一种方形网格上的二元混合有理插值函数,通过定义偏差商、偏逆差商和混合逆差商建立递推算法。构造的这种有理插值函数满足有理插值问题中所给的插值条件,并给出了插值的特征定理及其证明,进行了误差分析,最后给出的数值例子,验证了所给算法的有效性。     

与开工时间有关的加工时间的超前有奖迟后受罚的排序问题的动态规划算法

In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total weighted earliness award and tardiness penalty. Our aim is to find an optimal schedule so as to minimize the objective function. As the problem is NP-hard, some properties and polynomial time solvable cases of this problem are given. A dynamic programming algorithm for the general case of the problem is provided.     

一种C~2连续的三次样条插值方法

利用Bernstein多项式构造一种C~2连续的三次样条插值,证明其存在唯一性与一致收敛性,并给出误差上界的估计．与传统算法比较,避开了求解方程组的困难．