人民币兑美元汇率长期趋势分析及预测

旨在研究人民币汇率在相对较长时间内的趋势及更优的预测模型.基于时间序列分解原理将人民币兑美元汇率的时间序列分解为长期趋势及随机波动两部分,采用Logistic曲线拟合长期趋势,建立了包含长期趋势的复合预测模型.实证检验结果表明此预测模型的预测效果优于单一的ARIMA模型,根据分离的长期趋势,可以判定,人民币尚处于一个升值过程中,其未来的升值极限在5.5左右.     

ARIMA模型在新疆巴州梅毒疫情预测中的应用

搜集2008-2014年新疆巴音郭楞蒙古自治州(简称巴州)梅毒月发病数据,采用时间序列分解方法(Time Series Decomposition methods)探讨该地区梅毒月发病率的季节性,建立ARIMA(0,1,1)(1,0,1)_(12)时间序列模型,模型预测值的动态趋势与实际发病率基本吻合,平均绝对百分比误差MAPE=17.36,具有较高的预测精度,可以较好的预测短期内梅毒的变化趋势,为梅毒的预防控制措施提供可靠依据.     

仿射合成代数的三角分解

设是一个仿射箭图,它的极小虚单根为ｎ．设ｋ是一个有限域,记Ａ＝ｋ为ｋ上关于箭图的路代数,而记Ｃ(Ａ)为关于Ａ的合成代数．由Ｃ．Ｒｉｎｇｅｌ和Ｊ．Ｇｒｅｅｎ的工作,Ｃ(Ａ)揭示了Ａ的表示与量子群有密切的关系．文[１１]证明了对应于Ａ的不可分解表示可以分成预投射,正则,和预内射三个部分,Ｃ(Ａ)具有一个三角分解．[１１]中的证明需要假设维数向量为ｎ的拟单模存在,而对于|ｋ|＝２,是ｎ型和ｍ型(ｍ＝６,７,８)的情形,此假设不满足,本文的目的是给出一个简化的,而且不需要前面所提假设的证明．由此,得到一个与域ｋ无关的Ｃ(Ａ)的三角分解．     

基于分解—集成的铁路货运需求预测研究

铁路货运量受到多种因素影响,准确的预测可以为铁路行业未来规划的编制提供重要的参考依据,也可以使铁路部门制定符合当前货运市场的运输政策。货运量数据具有非线性、不平稳的特点,利用传统的单一预测模型进行预测,很难描述整体特征,预测精度有待提高。本文基于分解—集成的原则,利用变分模态分解算法将货运量分解为高频和低频模态,针对各模态特点,分别建立预测模型,将得到的预测结果加总起来作为最终货运量的预测值。实证表明,分解—集成预测方法与传统的单一预测模型相比,提高了预测的准确率,可以很好地应用在铁路货运量需求预测的研究中。     

大型稀疏矩阵的不完全因子分解法及预处理

本文对大型稀疏阵线性方程组的不完全因子分解及预处理法进行了研究。对对称正定阵和Ｌ阵分别提出了非对角元乘子不完全因子分解法的分解公式。对分解Ａ＝Ｍ－Ｎ，得到了当Ａ为对称正定时，Ｍ亦为对称正定，当Ａ为Ｌ阵时，分解为正规分裂等结果。并研究了预处理ＣＧ加速，最后的数值例子表明本文给出了的算法效果是良好的。     

图是圈的完全正矩阵

本文证明,图是围的完全正矩阵Ａ当比较矩阵Ｍ（Ａ）的行列式大于零时,恰有两个极小秩１分解,而当ｄｅｔＭ（Ａ）＝０时,恰有一个极小秩１分解．     

某些随机信号序列的合成与分解

本文讨论了几类随机信号序列的合成与分解问题。改进了ARMA序列的合成序列阶与参数的计算方法,提出了从ARMA(p,p)序列中分离出独立白噪声的充要条件。     

漫谈矩阵的分解

漫谈矩阵的分解杨凌（蚌埠教育学院）一、正定矩阵的分解定理１Ａ为正定矩阵的充分必要条件是：存在可逆矩阵Ｃ，使得：Ａ＝Ｃ′Ｃ．此结论，一般高等代数上均有证明，略去。定理２Ａ为正定矩阵的充分必要条件是存在实可逆上三角形矩阵Ｒ，使得：Ａ＝Ｒ′Ｒ。证１必要条件...     

解一类抽象积—微分方程的积分半群方法

在这篇文章内，研究一类含参数线性一算子族Ａ（ｔ）和线性算子Ｂ的积－微分方程，应用积分半群方法证明了该方程存在指数有界解，和含Ａ（ｔ），Ｂ的二阶微分方程存在指数有界和分解。这里Ａ（ｔ），Ｂ不必满足Ｈｉｌｌｅ－Ｙｏｓｉｄａ条件。     

求解二阶椭圆方程的区域分解方法──有限差分逼近

求解二阶椭圆方程的区域分解方法──有限差分逼近储德林，胡显承（清华大学应用数学系）ＴＨＥＤＯＭＡＩＮＤＥＣＯＭＰＯＳＩＴＩＯＮＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＳＥＣＯＮＤＯＲＤＥＲＥＬＬＩＰＴＩＣＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ...     

亏秩LS问题的解

运用范数、广义逆和矩阵分解等多种数学工具,对同一个线性最小二乘问题的不同最小二乘解之间的关系进行了多角度理解与证明.     

Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions

We provide two weakly convergent algorithms for finding a zero of the sum of a maximally monotone operator, a cocoercive operator, and the normal cone to a closed vector subspace of a real Hilbert space. The methods exploit the intrinsic structure of the problem by activating explicitly the cocoercive operator in the first step, and taking advantage of a vector space decomposition in the second step. The second step of the first method is a Douglas–Rachford iteration involving the maximally monotone operator and the normal cone. In the second method, it is a proximal step involving the partial inverse of the maximally monotone operator with respect to the vector subspace. Connections between the proposed methods and other methods in the literature are provided. Applications to monotone inclusions with finitely many maximally monotone operators and optimization problems are examined.     

Adaptive discretization for signal detection in statistical inverse problems

We discuss statistical tests in inverse problems when the original equation is replaced by a discretized one, i.e. a linear system of equations. Previous studies revealed that using the discretization level as regularizing procedure is possible, but its application is limited unless discretization is restricted to the singular value decomposition, see C. Marteau and P. Mathé, General regularization schemes for signal detection in inverse problems, 2013. General linear regularization may circumvent this, and we propose a regularization of the discretized equations. The discretization level may be chosen adaptively, which may save computational budget. This results in tests which are known to yield the optimal separation rate up to some constant in many cases.     

四元数矩阵的加权广义逆

利用四元数矩阵的加权奇异值分解 ,给出了四元数矩阵加权广义逆的显式表达 ,简化了应瓦金给出的相应结果 ,同时解答了有关的公开问题 .     

A truncated projected SVD method for linear discrete ill-posed problems

Truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. However, since the singular value decomposition of the matrix is independent of the right-hand side, there are linear discrete ill-posed problems for which this method fails to yield an accurate approximate solution. This paper describes a new approach to incorporating knowledge about properties of the desired solution into the solution process through an initial projection of the linear discrete ill-posed problem. The projected problem is solved by truncated singular value decomposition. Computed examples illustrate that suitably chosen projections can enhance the accuracy of the computed solution.     

带有变量选择过程的分类模型误差分析

偏倚一方差分析方法是在模型选择过程中权衡模型对现有样本解释程度和未知样本估计准确度的分析方法,目的是使选定的模型检验误差尽量小.在分类或回归过程中进行有效的变量筛选可以获得更准确的模型表达,但也会因此带来一定误差.提出"选择误差"的概念,用于刻画带有变量选择的分类问题中由于变量的某种选择方法所引起的误差.将分类问题的误差分解为偏倚—方差—选择误差进行研究,考察偏倚、方差和选择误差对分类问题的总误差所产生的影响.     

弹塑性有限变形力学的反逆渐近解法

最近几十年中,近代力学的非线性有限变形理论在概念与方法上有许多重要的进展([1],[2],[3]等).本文旨在说明自然拖带系描述法与Stokes-陈分解定理如何结合反过渐近解法于有效解答弹塑性有限变形力学问题应用至工程设计目的.文中举半平面冲压大变形为典型数值解例.     

Perturbation of the Weighted T-Core-EP Inverse of Tensors Based on the T-Product

In this paper,we extend the notion of the T-Schur decomposition to the weighted T-core-EP decomposition.Next,the weighted T-core-EP inverse of rectangular tensors is defined by a system,and its existence and uniqueness are obtained.Furthermore,the perturbation of the weighted T-core-EP inverse is studied under several conditions,and the relevant examples are provided to verify the perturbation bounds of the weighted T-core-EP inverse of tensors.     

态射的Γ-Drazin逆和柱心-幂零分解

讨论态射的Γ-Drazin逆.给出了态射的Γ-Drazin逆的一些性质和柱心-幂零分解.     

Cholesky decomposition of a positive semidefinite matrix with known kernel

The Cholesky decomposition of a symmetric positive semidefinite matrix A is a useful tool for solving the related consistent system of linear equations or evaluating the action of a generalized inverse, especially when A is relatively large and sparse. To use the Cholesky decomposition effectively, it is necessary to identify reliably the positions of zero rows or columns of the factors and to choose these positions so that the nonsingular submatrix of A of the maximal rank is reasonably conditioned. The point of this note is to show how to exploit information about the kernel of A to accomplish both tasks. The results are illustrated by numerical experiments.