In the paper,for solving large sparse vertical linear complementarity problems,a two-step modulus-based matrix synchronous multisplitting parallel iteration method is construct-ed by using two-step multisplitting technique.The new method can be viewed as a gener-alization of the modulus-based matrix synchronous multisplitting iterative method and the two-step modulus-based matrix splitting iterative method in the existing literatures.Fur-thermore,under the assumption that the system matrices are H+-matrices,the convergence analysis of the proposed method is given,and the convergence domain of the parameter matrix is obtained,which extends the convergence results of the existing methods.Finally,numerical experiments are carried out under the OpenMP framework for two numerical ex-amples in the existing literatures.Numerical results show that the two-step multisplitting technique can improve the computational efficiency of the existing methods.

根据《高等学校课程思政建设指导纲要》的精神,在"数据分析"课程教学中把马克思主义立场观点方法的教育与科学精神的培养相结合,对"数据分析"课程思政建设改革进行探索研究.从数据案例的背景特点,发掘其中的思政元素,组织思政协同教学;结合课程实训加强学生对数据案例的体验以及强化思政元素的融入.

以Galois理论为导向,对数学与应用数学本科专业的抽象代数课程进行教学改革,在更高的理论框架下展现课程主体知识的关联和延伸,使学生进一步明确课程目标、激发兴趣以及拓宽视野,提高学生学习动力和提升教学效果,使学习更有深度、广度和宽度.

在红利有界的条件下,讨论了复合二项对偶模型中带比例交易费再注资且分红贴现利率随机变化的最优分红问题;运用压缩映射不动点原理证明了该最优分红问题的最优值函数是一个离散的HJB方程的唯一解,得到了最优分红策略和最优值函数的计算方法;根据分红策略的一些性质,得到了该最优值函数的可无限逼近的上界和下界,并采用了Bellman递归算法得到最优值函数和最优分红策略的数值解,从而得到最优分红算法.数值实例结果表明:该最优分红策略是有效的.这为公司的决策者在兼顾公司正常运营和股东利益而进行红利决策时提供了理论依据.

在数学模型、数值分析、数学软件等信息与计算科学专业课程中渗透PageRank的数学思想,可以用来在教学过程中形成链条式的教学模式,使学生进一步明确学习目标、激发学习兴趣以及拓展学习视野,提高学生学习动力和提升教学效果,使学习更有深度、广度和宽度,进而辐射科学计算后续相关专业课程.

以应用型人才培养为导向,给出了把稀疏矩阵理论引入"数值分析"课程的教学策略.针对"数值分析"课程内容中与稀疏矩阵相关的数值线性代数内容,从求解线性方程组的直接法、求解线性方程组的迭代法和特征值计算3方面,结合稀疏矩阵与相关知识重难点的关联,通过MATLAB实例展示了稀疏矩阵教学方法的实施策略.新教学策略的引入,可以完善课程教学体系,使课程教学更好地适应大数据时代的新要求.

基于非负矩阵的特征值理论,研究了Google搜索模型中阻尼系数和个性化向量对PageRank排序结果的影响,建立了两个相应的排序模型,并通过数值例子验证所得到的结果.

首先建立综合评价指标体系用于评价长江经济带沿岸各城市的投资环境.在此基础上,采用聚类分析和因子分析法找到核心辐射城市及各城市发展水平排名.再结合熵权法及有序probit模型得到各城市的综合指数,并对模型进行了灵敏性分析.除了上海外,其他各城市的投资环境指数普遍不高,地区发展极不平衡.模型通过了检验,非常的稳健.最后提出了相应的建议及对策.

The perturbation bounds of the joint stationary distribution vector of the high-order multivariate Markov chains are established.By the properties of the left and right eigenvectors of the probability transition matrix of the high-order multivariate Markov chains,the perturbation bound of the joint stationary distribution vector of the high-order multivariate Markov chains is obtained,which generalizes the results of the existing perturbation bounds of the joint stationary distribution vector of one-order multivariate Markov chains.Then the computational perturbation bound is given by the characteristic of the probability transition matrix of the high-order multivariate Markov chains,which also generalizes the corresponding perturbation bound of the joint stationary distribution vector of oneorder multivariate Markov chains.Moreover,considering the perturbation in the item of the joint stationary distribution vector of high-order multivariate Markov chains,the perturbation bound of the joint stationary distribution vector based on component form is established by Paz's inequality,to observe the perturbation of a state in a chain of the high-order multivariate Markov chains.

给出求解一类投资组合问题的半光滑Newton法,并对算法进行收敛性分析,数值例子表明新方法的高效率.

On the basis of the theory of derivative of matrix function,the derivative of eigenvalue of real symmetry matrix,which is perturbed by a symmetry matrix,is showed.Then another method to prove Wielandt-Hoffman theorem is given.

The set of full rank matrices is proved to be open and dense,using the theory of singular value decompo- sition.The effect of the rank of a matrix by disturbance of its items is explained,and a relationship between the set of full rank matrices and the set of rank deficiency matrices is showed.