k步转移矩阵的频谱插值计算法

本较全面研究了系统状态转移矩阵的各种计算方法，在分析这些方法在实用计算中各自特点的同时，提出了较为有效的频谱插值计算法。作为应用与比较，中给出了几十特殊转移矩阵的计算结果。     

基于修正转移概率矩阵的Markov方法在企业人才结构预测中的应用

预测企业人才结构的变化;修正转移概率矩阵的Markov预测方法;用修正转移概率矩阵的Markov模型针对人才结构进行定量预测与分析,对历史数据样本数量要求不多,并且计算简便;获取的计算结果更具客观性、真实性.     

一种估算马尔柯夫状态转移概率矩阵的新方法

在现有文献研究的基础上,对马尔柯夫状态转移概率矩阵估算方法又作了进一步研究,根据马尔柯夫状态转移概率矩阵的性质和特点,提出了一种新的估算方法.方法首先构造了一个以相对误差绝对值之和最小为目标,以某一状态转移到其他状态的概率之和等于1以及状态转移概率不小于零为约束条件的优化模型.在此基础上,通过变量替换,将该模型转化为线性规划模型.由于线性规划模型不仅能够求得解析解,而且有现成的求解软件,因此不但便于问题求解,而且更加方便、可靠.最后进行了示例计算,验证了给出的马尔柯夫状态转移概率矩阵优化算法的可行性和正确性.     

基于马尔可夫模型的我国东、中、西部的产业结构预测

应用马尔可夫预测方法对我国东、中、西部产业结构预测问题进行研究,并给出了其马尔可夫的状态转移概率矩阵的估算模型,经计算结果表明此方法具有较高的预测精度,并应用此方法预测了我国2009年和2010年的东、中、西部的产业结构.     

两类递归图的Tutte多项式

本文用转移矩阵给出了C2×Pn和N2∨Pn的Tutte多项式的公式,根据公式设计了M ap le程序,该程序对每个固定的整数n 2都能计算出C2×Pn和N2∨Pn的Tutte多项式.     

人卫精密定轨中的算法问题

对当今人卫精密定轨问题 ,由于力学模型复杂 ,精密星历和状态转移矩阵的计算均采用数值方法 ,这就需要积分两组常微分方程 .现给出一个方法可避免数值求解两组常微分方程 ,并以实际算例证实了算法的有效性 .     

药动学随机过程模型

用随机过程的方法 ,建立了一种用于分析药物在体内吸收、分布、消除的模型 ,推导了该模型的高阶转移概率矩阵 ,并对应用问题进行了讨论 .     

标准三点转移函数

一般的三点转移函数(TTF),不便用转移矩阵来表示.对于标准三点转移函数(STTF),引入了3类联络矩阵,研究了它们的一般特性和基本关系,给出了常值型标准三点转移函数的生成方法和状态对称型标准三点转移函数的一般表达形式.     

e~(At)四种计算方法的比较

状态转移矩阵eAt在现代控制理论与工程技术以及常系数微分方程组理论中有着非常重要的应用.通过一个实例,给出计算状态转移矩阵eAt的四种不同的方法:矩阵指数函数展开法,Jordan标准形法,待定系数法,Laplace变换法.笔者论述了各种计算方法的基本步骤及计算的难点与要点,经过分析对比,最后给出最优选择.     

马尔科夫链在对话信息识别犯罪中的应用

通过对话信息进行识别分析,构造了罪犯嫌疑度的一种确定方法.首先对人群的对话模式进行了分类,确定了9种对话类型下罪犯的嫌疑程度权向量.然后计算出话题权向量的初始值,再引入修正向量对话题权向量进行修正.最后利用马尔科夫法对人员犯罪的嫌疑度进行了分析.通过每个人传递敏感信息的信息量,构造概率转移矩阵,从而计算出在长期作用下将会出现的稳定状态,即稳定状态时人员犯罪的嫌疑度.     

Algebraic transition matrices in the Conley index theory

We introduce the concept of an algebraic transition matrix. These are degree zero isomorphisms which are upper triangular with respect to a partial order. It is shown that all connection matrices of a Morse decomposition for which the partial order is a series-parallel admissible order are related via a conjugation with one of these transition matrices. This result is then restated in the form of an existence theorem for global bifurcations. Simple examples of how these results can be applied are also presented.

     

成绩转移权系数法在教学效果评价中的应用

研究了评价教学效果的成绩转移权系数法,给出了成绩转移权系数法的评价步骤,并通过具体实例验证了该法的合理性。     

An improved method for the computation of the Moore-Penrose inverse matrix

In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better accuracy than the already proposed methods, while works for full and sparse matrices.     

多个相异性矩阵的数据分析

本文给出了分析多个相异性矩阵的三种方法.首先找到了一种图表示,使我们对所有相异性矩阵有一个总体的了解;其次定义了一个新的相异性矩阵,它可以看作是对所有原始相异性矩阵的一个折衷处理;最后提出了一种MIMU方法.在文中我们还对由上述方法得到的坐标图进行了比较.     

随机环境中分枝q-过程

引进了机环境中一致马氏过程,随机分枝q-矩阵和随机环境中分枝q-过程.给了随机环境中分枝q-过程存在性和唯一性的充分条件.最后证明了任意随机分枝转移密度矩阵都是零流入的.     

Sufficient embedding conditions for three-state discrete-time Markov chains with real eigenvalues

Within the set of discrete-time Markov chains, a Markov chain is embeddable in case its transition matrix has at least one root that is a stochastic matrix. The present paper examines the embedding problem for discrete-time Markov chains with three states and with real eigenvalues. Sufficient embedding conditions are proved for diagonalizable transition matrices as well as for non-diagonalizable transition matrices and for all possible configurations regarding the sign of the eigenvalues. The embedding conditions are formulated in terms of the projections and the spectral decomposition of the transition matrix.     

Block-successive approximation for a discounted Markov decision model

In this paper we suggest a new successive approximation method to compute the optimal discounted reward for finite state and action, discrete time, discounted Markov decision chains. The method is based on a block partitioning of the (stochastic) matrices corresponding to the stationary policies. The method is particularly attractive when the transition matrices are jointly nearly decomposable or nearly completely decomposable.     

Analysis of the Structured Total Least Squares Problem for Hankel/Toeplitz Matrices

The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) approach when structured matrices are involved and a similarly structured rank deficient approximation of that matrix is desired. In many of those cases the STLS approach yields a Maximum Likelihood (ML) estimate as opposed to, e.g., TLS.In this paper we analyze the STLS problem for Hankel matrices (the theory can be extended in a straightforward way to Toeplitz matrices, block Hankel and block Toeplitz matrices). Using a particular parametrisation of rank-deficient Hankel matrices, we show that this STLS problem suffers from multiple local minima, the properties of which depend on the parameters of the new parametrisation. The latter observation makes initial estimates an important issue in STLS problems and a new initialization method is proposed. The new initialization method is applied to a speech compression example and the results confirm the improved performance compared to other previously proposed initialization methods.     

Factorization of the transition matrix for the general Jacobi system

The Jacobi system on a full‐line lattice is considered when it contains additional weight factors. A factorization formula is derived expressing the scattering from such a generalized Jacobi system in terms of the scattering from its fragments. This is performed by writing the transition matrix for the generalized Jacobi system as an ordered matrix product of the transition matrices corresponding to its fragments. The resulting factorization formula resembles the factorization formula for the Schrödinger equation on the full line. Copyright © 2016 John Wiley & Sons, Ltd.     

Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis

For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end, we develop a method for obtaining uniform asymptotics, with respect to the spectral parameter, of the generalized eigenvectors. Our technique can be applied to a wide range of Jacobi matrices.