通货紧缩现象的自组织方法研究

本文运用自组织方法建模研究中国通货紧缩现象的成因及其治理对策 ,定量分析各因素的影响力强弱并给出相关政策建议     

基于灰色灾变模型的通货紧缩预测

针对未来期间通货紧缩是否存在的分歧以及通货紧缩可能存在的危害性,利用灰色灾变预测模型结合中国通货紧缩的小样本数据,预测未来通货紧缩发生的日期,预测结果显示通货紧缩约在2020年前后出现,预测结果一方面意味着当前应该审慎选择货币政策和财政政策,另一方面在2020年前后应该积极调整货币政策和财政政策,避免通货紧缩的出现可能给经济运行带来的负面性影响.     

有效需求与通货紧缩的统计关系研究

本文通过对有效需求一物价指数统计模型的研究 ,估计出了有效需求方程 ,并且通过对模型的估计结果分析得出如下结论 :物价指数对有效需求的影响是显著的 :通货紧缩、物价指数持续走低是有效需求不足的主要原因 ,治理通货紧缩应该是解决我国有效需求不足的主要任务。     

社区大学数学建模教学及其评估

20世纪以来 ,数学的应用已深入到所有重要学科 ,数学建模也以其广泛的参与性促进了科学技术与经济建设的紧密结合 .我国普通高校数学建模竞赛活动发展迅速 ,而社区大学数学建模教学进展缓慢 .1 996年 ,在三维教学模式研究的基础上 ,丰台职大开设了数学建模新课 ,为北京市社区大学数学建模教学及其评估提供了成功的案例     

精心选择案例 建设新形态教材——《数学模型》(第五版)简介

正20世纪80年代初数学建模进入我国大学课堂,90年代初数学建模竞赛在我国蓬勃兴起.随着数学建模课程教学和竞赛活动的迅速开展,各种形式的数学建模教材及辅助读物如雨后春笋般涌现,30多年来正式出版的大约有200本(据2001年统计在150本以上),这大概是任何其他一门大学数学课程无法企及的.     

高中数学建模中教师问题初探

教育部2003年颁布的《普通高中数学课程标准（实验）》口是我国中学数学应用与建模发展的一个里程碑，它把数学建模纳入了内容标准中，这标志着数学建模正式进入我国高中数学．但是我们应该看到，随着高中数学课程改革的不断深入，在更多的中学数学教师参与到数学建模活动的探索之中，     

卷首语

<正>不知不觉,《数学建模及其应用》已经进入到第三个年头。《数学建模及其应用》是关于数学建模及其应用的专门学术刊物。它的诞生是与全国大学生数学建模竞赛在我国蓬勃开展分不开的。正因为如此,在刊物的创办初期,编委会应该依靠全国大学生数学建模竞赛组委会,结合全国大学生数学建模竞赛这一有着重要影响的赛事,调动全国参与数学建模竞赛的广大师生的积极性,将《数学建模及其应用》办成一个让参与数学     

“闲钱”活用

2009年初,几乎所有人都相信在这一年里,实体经济将会面临更大的考验,甚至陷入通货紧缩的泥潭。那时,企业家们最担心的问题,是如何筹集资金。     

我国货币政策非对称反应的实证检验

本文运用弹性非线性推断方法研究我国货币政策反应函数的非线性特征,以新的视角解释和分析我国中央银行的货币政策行为。研究结果表明,我国货币政策反应函数存在显著的非线性特征,突出表现为利率对通货膨胀和通货紧缩的非对称反应,即在高通胀时期中央银行实施严厉的利率政策以降低通货膨胀;而在低通胀时期实施稳健的货币政策,根据通胀变化线性微调短期利率。研究结果还表明,这种非线性特征可能主要源于中央银行对通胀正负偏离的非对称偏好,并有部分来自其对通胀缺口和产出缺口之间相互影响的政策反应。     

形成和发展中学生数学建模核心素养的几点做法北大核心

目前我国普通高中数学课程标准和新的教材都将数学建模内容列入学生必修内容;但在实际教学中,教师和学生对数学建模这种具有多样性、新奇性的学习形式存在一定的畏难心理,在数学建模学习的选题、开题、做题、结题四个环节上都会遇到困难.多年来,我校为配合参加上海市中学生数学知识应用竞赛,对数学建模教学进行了积极的探索,以下几点做法可以帮助中学生克服数学建模学习中的困难,有利于中学生数学建模核心素养的形成.     

An Implicitly Restarted Block Arnoldi Method in a Vector-Wise Fashion

In this paper, we develop an implicitly restarted block Arnoldi algorithm in a vector-wise fashion. The vector-wise construction greatly simplifies both the detection of necessary deflation and the actual deflation itself, so it is preferable to the block-wise construction. The numerical experiment shows that our algorithm is effective.     

Rnyleigh商理论应用于矩阵特征值的收缩技术

This paper analyzes the influences of the deflation on the accuracy of the com pared eigenvalues of matrix. Based on the Rayleigh quotient theory, we proved that the influences, Generally speaking, are less important.     

广义特征值问题近似收缩对组误差的残量界限

近年来,人们对矩阵不变子空间和矩阵束的广义不变子空间的计算颇为注意,关于误差和摄动理论的研究也比较深入.对于单个矩阵的情况,[4]中研究了非规范矩阵的近似特征组的残量界限,与大多数已有的误差估计不同,这个界限是可计算的,因而便于     

Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations

The solution of a large-scale Sylvester matrix equation plays an important role in control and large scientific computations. In this paper, we are interested in the large Sylvester matrix equation with large dimensionA and small dimension B, and a popular approach is to use the global Krylov subspace method. In this paper, we propose three new algorithms for this problem. We first consider the global GMRES algorithm with weighting strategy, which can be viewed as a precondition method. We present three new schemes to update the weighting matrix during iterations. Due to the growth of memory requirements and computational cost, it is necessary to restart the algorithm effectively. The deflation strategy is efficient for the solution of large linear systems and large eigenvalue problems; to the best of our knowledge, little work is done on applying deflation to the (weighted) global GMRES algorithm for large Sylvester matrix equations. We then consider how to combine the weighting strategy with deflated restarting, and propose a weighted global GMRES algorithm with deflation for solving large Sylvester matrix equations. In particular, we are interested in the global GMRES algorithm with deflation, which can be viewed as a special case when the weighted matrix is chosen as the identity. Theoretical analysis is given to show rationality of the new algorithms. Numerical experiments illustrate the numerical behavior of the proposed algorithms.

     

Two variations of Boas–Fu–Straube’s deflation identity

In this article, we investigate deflation type identities of the Bergman kernel functions. The first identity of this kind was obtained by Boas, Fu, and Straube in 1999. It was generalized by the author of the present article in 2015. In 2017, Beberok also obtained a deflation type identity for certain Reinhardt domains. In this article, we introduce the Roos domains which include all domains considered in these three works as special cases. We establish two variations of deflation type identities for Roos domains.     

Convergence acceleration of preconditioned conjugate gradient solver based on error vector sampling for a sequence of linear systems

In this article, we focus on solving a sequence of linear systems that have identical (or similar) coefficient matrices. For this type of problem, we investigate subspace correction (SC) and deflation methods, which use an auxiliary matrix (subspace) to accelerate the convergence of the iterative method. In practical simulations, these acceleration methods typically work well when the range of the auxiliary matrix contains eigenspaces corresponding to small eigenvalues of the coefficient matrix. We develop a new algebraic auxiliary matrix construction method based on error vector sampling in which eigenvectors with small eigenvalues are efficiently identified in the solution process. We use the generated auxiliary matrix for convergence acceleration in the following solution step. Numerical tests confirm that both SC and deflation methods with the auxiliary matrix can accelerate the solution process of the iterative solver. Furthermore, we examine the applicability of our technique to the estimation of the condition number of the coefficient matrix. We also present the algorithm of the preconditioned conjugate gradient method with condition number estimation.     

陀螺系统特征值问题的收缩Jacobi-Davidson方法

本文研究陀螺系统特征值问题的Jacobi-Davidson方法. 利用陀螺系统的结构性质,给出了求解Jacobi-Davidson方法中校正方程的有效方法. 基于非等价低秩收缩技术,给出了计算陀螺系统一些特征值的收缩Jacobi-Davidson方法. 数值结果表明本文所给算法是有效的.     

Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems

In this paper, we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations. Theoretical analysis shows that with the deflation technique, the new residual of shifted restarted FOM is still collinear with each other. Hence, the new approach can solve the shifted systems simultaneously based on the same Krylov subspace. Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.     

求解陀螺系统特征值问题的收缩二阶Lanczos方法

本文研究陀螺系统特征值问题的数值解法,利用反对称矩阵Lanczos算法,提出了求解陀螺系统特征值问题的二阶Lanczos方法.基于提出的陀螺系统特征值问题的非等价低秩收缩技术,给出了计算陀螺系统极端特征值的收缩二阶Lanczos方法.数值结果说明了算法的有效性.