隐式重新启动的Lanczos算法在模型降阶中的应用

主要研究了一种隐式重新启动的L anczos算法在模型降阶中的应用.分析了由这个算法得到的降价后的模型的一些性质,对于一个n阶稳定的线性时不变系统,模型降阶的思想是寻找一个m阶转换函数来近似原系统的n阶转换函数H(s),其中n m.传统的kry lov子空间方法仅仅产生一个不稳定的实现,并且在低频处的误差较大,本文所考虑的隐式重新启动的L anczos方法,能较好的解决上述两个问题.     

对含有整数最小素因子的倒数的某些和的估计

设p(n)表示整数n>1的最小素因子.本文得到了(?),v≥0的渐近式,此处f_v(n)是一类数论函数.     

参数曲线的分段近似隐式化

曲线的参数形式和隐式形式之间的相互转化在CAGD和造型中起着重要的作用,将参数形式的曲线转化为代数形式的曲线的过程称为隐式化.由于复杂参数曲线的精确隐式化比较困难,因此近似隐式化就显得非常重要.基于隐函数样条与异度隐函数样条,作者提出了参数曲线分段近似隐式化方法,并给出具体算法.通过实例对比,说明了此方法的简洁性和有效性.     

关于Smarandache函数与Riemann zeta-函数

对任意正整数n,著名的Smarandache函数S(n)定义为最小的正整数m使得n|m!.即S(n)=min{m∶m ∈N,n|m!).本文的主要目的是利用初等方法研究一类包含S(n)的Dirichlet级数与Riemann zeta-函数之间的关系,并得到了一个有趣的恒等式.     

Cauchy中值定理与Leibniz公式的推广

引入辅助函数的方法可将Cauchy中值定理推广到高阶形式,即两函数n阶Taylor展开误差的比值等于在某点两函数(n+1)阶导数比值的形式;用数学归纳法可将Leibniz公式中函数的个数推广至任意有限多个.     

法向最小二乘法

<正> 通常的最小二乘法是以||·||_2z为准则,本文提出一种以数据点到拟合曲线的法向距离之平方和为准则的法向最小二乘法。设有m个数据点(x_i,y_i)(i=1,2,…m),n个基函数_f(x)(j=1,2,…,n),线性最小二乘拟合曲线函数为     

迭代·递归·一类函数的周期性

求已知函数f(x)的n次迭代式f(f(…(f(x))))的明显表达式,是一个古老、有趣而又困难的问题。本文先指出函数迭代与递归数列的关系;然后给出求函数迭代式的一种简便方法——递归法,最后探讨一类函数的周期性。一、设f(x)是定义在D上的函数,记     

浅谈数据资料的处理和函数拟合

为了研究解决一个实际问题,我们往往要从一组观察得到的数据(xi,yi),i=1,2,…,n中寻找自变量x与因变量y之间的函数关系.最小二乘法是寻找适当函数关系即数据拟合的一个常用的方法.……     

Morgan-Mercer-Flodin模型和Weibull模型的拟合

Morgan-Mercer-Flodin模型和 Weibull模型是两个著名的四参数 S形生长模型 .在一定的正则变换下 ,它们的隐函数方程及未线性化参数与拐点特征之间的联系都非常相似 .从而可用完全相同的方法对它们的未线性化参数初始值进行搜索 ,以拟合隐函数曲线的 GNL法对它们进行最小二乘拟合 .还用实例对这种算法进行了验证 .     

Non-Probabilistic Structural Reliability Analysis Integrating the PSO and the Kriging Model北大核心CSCD

针对复杂结构可靠性分析中面临的隐式功能函数和小样本问题,提出了一种粒子群优化和Kriging模型相结合的结构非概率可靠性分析方法。采用多维椭球描述结构不确定参数,运用粒子群优化对模型相关参数进行求解,并构建隐式功能函数的Kriging模型进行可靠性分析。三个算例结果表明所提方法有效可行,精度和效率均优于基于Kriging模型的非概率可靠性分析方法。     

用LSD法再探泥石流地貌要素之隐式关系

藉助MATLAB工具,对泥石流沟的六个地貌要素之流域面积、主沟长、切割度、沟口高程、流域高差和沟床比降等,一起用最小平方距离法(LSD)进行了初步处理分析之探讨:建立了线性相关的回归方程,并与用最小二乘法(LS)得到的线性回归方程进行比较,一些参数的估计值得到了改善。     

The variable projection algorithm in time-resolved spectroscopy,microscopy and mass spectrometry applications

Nonlinear least squares optimization problems in which the parameters can be partitioned into two sets such that optimal estimates of parameters in one set are easy to solve for given fixed values of the parameters in the other set are common in practice. Particularly ubiquitous are data fitting problems in which the model function is a linear combination of nonlinear functions, which may be addressed with the variable projection algorithm due to Golub and Pereyra. In this paper we review variable projection, with special emphasis on its application to matrix data. The generalization of the algorithm to separable problems in which the linear coefficients of the nonlinear functions are subject to constraints is also discussed. Variable projection has been instrumental for model-based data analysis in multi-way spectroscopy, time-resolved microscopy and gas or liquid chromatography mass spectrometry, and we give an overview of applications in these domains, illustrated by brief case studies.     

Linear ordinal quasi-symmetry model and decomposition of symmetry for multi-way tables

For multi-way tables with same categories, Bhapkar and Darroch [4] and Agresti [2], p. 440, considered the general order quasi-symmetry model and the ordinal quasi-symmetry model, respectively. Yamamoto, Iwashita and Tomizawa [16] considered the three kinds of linear ordinal quasi-symmetry models, which are special cases of the first and second order quasi-symmetry models. For multi-way tables with same ordinal categories, the present paper proposes the general linear ordinal quasi-symmetry models, which are special cases of the general order quasi-symmetry model, and gives new decomposition of the symmetry model. Moreover it is shown that the likelihood ratio statistic for testing goodness-of-fit of the symmetry model is asymptotically equivalent to the sum of those for testing goodness-of-fit of the decomposed models.     

广义交替近似梯度算法的线性收敛分析

针对两个可分凸函数的和在线性约束下的极小化问题,在交替方向法的框架下,提出广义的交替近似梯度算法.在一定的条件下,该算法具有全局及线性收敛性.数值实验表明该算法有好的数值表现.     

A memetic algorithm approach for solving the multidimensional multi-way number partitioning problem

In this paper, we describe a generalization of the multidimensional two-way number partitioning problem (MDTWNPP) where a set of vectors has to be partitioned into p sets (parts) such that the sums per every coordinate should be exactly or approximately equal. We will call this generalization the multidimensional multi-way number partitioning problem (MDMWNPP). Also, an efficient memetic algorithm (MA) heuristic is developed to solve the multidimensional multi-way number partitioning problem obtained by combining a genetic algorithm (GA) with a powerful local search (LS) procedure. The performances of our memetic algorithm have been compared with the existing numerical results obtained by CPLEX based on an integer linear programming formulation of the problem. The solution reveals that our proposed methodology performs very well in terms of both quality of the solutions obtained and the computational time compared with the previous method of solving the multidimensional two-way number partitioning problem.     

Maximum likelihood estimation of covariance matrices under simple tree ordering

The closed-form maximum likelihood estimators for the completely balanced multivariate one-way random effect model are obtained by Anderson et al. (Ann. Statist. 14 (1986) 405). It remains open whether there exist the closed-form maximum likelihood estimators for the more general completely balanced multivariate multi-way random effects models. In this paper, a new parameterization technique for covariance matrices is used to grasp the inside structure of likelihood function so that the maximum likelihood equations can be dramatically simplified. As such we obtain the closed-form maximum likelihood estimators of covariance matrices for Wishart density functions over the simple tree ordering set, which can then be applied to get the maximum likelihood estimators for the completely balanced multivariate multi-way random effects models without interactions.     

Estimation of Wishart mean matrices under simple tree ordering

For Wishart density functions, we study the risk dominance problems of the restricted maximum likelihood estimators of mean matrices with respect to the Kullback-Leibler loss function over restricted parameter space under the simple tree ordering set. The results are directly applied to the estimation of covariance matrices for the completely balanced multivariate multi-way random effects models without interactions.     

构造三角样条小波的一种新方法

首先给出了三角样条函数及其性质,然后在此基础上给出了一种构造三角样条小波的新方法.该方法简单易行,而且构造出的小波具有许多良好的性质,如对称性(具有线性相位或广义线性相位)、良好的时频局部特性、短支集及半正交性等,这些对信号处理是非常重要的.     

The use of Chebyshev cardinal functions for solution of the second‐order one‐dimensional telegraph equation

A numerical technique is presented for the solution of the second order one‐dimensional linear hyperbolic equation. This method uses the Chebyshev cardinal functions. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem is reduced to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions

This article proposes a simple efficient direct method for solving Volterra integral equation of the first kind. By using block-pulse functions and their operational matrix of integration, first kind integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. Some examples are presented to illustrate efficiency and accuracy of the proposed method.