一类完全消耗阵的图解法和矩阵解法

本文对一类完全消耗阵提出了图解法和矩阵解法 .     

静态非线性投入产出模型的若干数学问题

SomeMathematicalProblemsoftheNolinearOutput-InputfortheStaticModelHeJianminWangDongHaoJinliangInstituteofSystemsScience,AcademicSinica100080一、非线性投入产出模型的提出建立在同质性和比例性假定上的列昂惕夫投入产出模型，假定了每一部门只有单一的消耗结构并只生产一种产品，直接消耗系数不变且非负。因假定极大地简化了经济现实，它在解决短期经济和社会问题方面取得了成功，但在长期预测和计划等方面并不十分准确。为使投入产出模型能更好地进行长期预测，人们提出各种方法来修正直接消耗系数。例如：1.专家评估法…     

关于子式矩阵的行列式

讨论子式阵及伴随阵的行列式,得到了高阶伴随阵行列式的一般公式.我们的结果改进了文献中的相应结果.     

关于四个三幂等阵线性组合的可逆性和群逆

本文研究了四个三幂等阵线性组合的可逆性及群逆.利用矩阵分解的方法,获得了它们可逆及群逆的一些条件,并得到其逆和群逆的计算公式,这些结论完善了k幂等阵可逆性理论.     

群逆和Drazin逆的一种新的表达式及其应用

本文研究了群逆的存在条件及群逆、Drazin逆的表示与计算.利用行列式表示方法,得到了群逆存在的充要条件,给出了群逆的与原矩阵最大非奇异子阵有关的表达式.并推广到Drazin逆.为群逆和Drazin逆的计算提供了一类新的算法.     

多重嵌套的可计算非线性动态投入产出模型及其平衡增长解

给出多重嵌套的可计算非线性动态投入产出模型,并给出相应的价格、利润率、产出结构、增长率的平衡增长解计算公式.从本文给出的模型可以看出非线性投入产出模型可以有无穷多种不同形式,其中只有1种为众所周知的列昂惕夫线性投入产出模型.本文模型的重要意义在于它是线性投入产出模型与CGE（可计算一般均衡）模型的统一.它既克服了线性投入产出模型资本与劳动不可替代的缺点,又可方便地求解动态CGE的平衡增长解.     

广义酉矩阵与广义Hermite矩阵

给出了广义酉矩阵与广义(斜)Hermite矩阵的概念，研究了它们的性质及其与酉阵、共轭辛阵、Hermite阵、Hamilton及广义逆矩阵之间的联系；取得了许多新的结果；推广了酉矩阵、Hermite阵与斜Hermite阵间的相应结果，特别将正交阵的广义Cayley分解推广到了广义酉矩阵上；将各类酉矩阵、Hermite矩阵及广义逆矩阵统一了起来．     

奇异协方差阵下有效前沿及有效组合的解析解

利用广义逆矩阵研究了协方差阵奇异时的投资组合问题,突破了传统方法中要求协方差阵可逆的限制,得到了证券市场存在有效组合的充要条件,并给出了有效前沿和有效组合的解析解,成功地推广了经典Markowitz模型,同时还将有助于证券组合有效子集的深入研究.     

子空间上的对称正定及对称半正定阵的左右特征值反问题

文[1][2][3]中讨论AX＝B的对称阵逆特征值问题，文[4][5][6]中讨论了半正定阵的逆特征值问题。本文讨论了空间了子空间上的对称正定及对称半正定阵的左右特征值反问题，给出了解存在的充分条件及解的表达式。     

RAS法真实误差的实证研究

RAS法为更新投入产出表的主要非调查方法之一,作为非调查方法,更新误差的大小决定了方法的应用价值,但传统的误差估计方法由于在设计上的缺陷,其估计结果在本质上是RAS法误差的下限.本文利用1992、1997、2002年中国投入产出表及1997、2002年常规统计数据首次对实际应用中RAS法的真实误差进行了实证研究.结果表明:传统的误差估计方法显示使用RAS法将使投入产出系数的平均误差下降17.84%;而在实际应用中,使用RAS法只能使投入产出系数的平均误差下降5.92%.因此,传统的误差估计方法会非常显著低估RAS法的真实误差.从而夸大了RAS法的应用价值.     

The foundation of the grey matrix and the grey input–output analysis

The grey systems theory aims at the objects that their information is inadequate and this situation is general in reality. It has been urgent work to study the uncertain problems using the missing information. With the help of the simple introduction of grey systems theory, we further study the covered operation and get some calculation rules about grey number. The definition of grey matrix (GM) and its covered operation are proposed. Particularly, some results of the inverse grey matrix are obtained. Also with the help of the proposed grey matrix theory and the traditional input–output analysis, we propose the grey input–output analysis. The most important results are the computational formulas and their rigorous proofs of the matrix-covered set of the inverse grey Leontief coefficient’s matrix. It provides an effective tool to study an economic system by the input–output analysis under the uncertain situation. The modified case verifies the effectiveness of our methodology.     

灰色关联度分析在投入产出关联度中的应用

产业经济学常用投入产出方法中的影响力系数和感应度系数来评价部门的拉动和推动作用,从而作为确定国民经济中关键部门最重要的参考指标。本文针对影响力系数和感应度系数的缺陷,采用灰色关联度曲线相似的思想对中国1997年17部门的投入产出表作了实证分析,并和传统的方法作了比较,结果表明,用本方法确定关键部门更符合实际,具有重要的参考价值。     

不确定性系统投入产出分析模型及预测

本综述了不确定性经济系统投入产出模型中直接消耗系数矩阵A=(aij）n的预测方法-RAS方法及其改进方法,定义了灰直接消耗系G（aij）,给出了不确定性经济系统灰色投入产出模型。     

推广的实用华氏宏观经济增长模型及参数估计

从我国当前经济系统中消费、投资和出口的实际作用和现有的国民经济数据统计口径出发,借助于L eon tief平衡模型,对经典的华氏经济增长模型进行了改进,推广了一类具有实用性的华氏宏观经济增长模型,论证了该经济增长模型存在实现宏观经济均衡增长的条件,并且给出了利用实际经济数据估算投入系数的方法,同时指出了推广的华氏宏观经济增长模型和实用宏观经济增长模型、经典华氏经济增长模型之间的关系.     

An efficient method for computing the inverse of arrowhead matrices

In this paper we propose a simple and effective method to find the inverse of arrowhead matrices which often appear in wide areas of applied science and engineering such as wireless communications systems, molecular physics, oscillators vibrationally coupled with Fermi liquid, and eigenvalue problems. A modified Sherman–Morrison inverse matrix method is proposed for computing the inverse of an arrowhead matrix. The effectiveness of the proposed method is illustrated and numerical results are presented along with comparative results.     

Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin inverse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.     

Determination of reflector surfaces from near-field scattering data II. Numerical solution

Let be a nonisotropic point source of light, and the power intensity of this source in direction . Suppose that the light rays emitted by the source through an aperture fall on a perfectly reflecting surface and reflect off it so that the reflected rays illuminate a closed domain on some plane with intensity . The inverse problem consists of constructing the reflector surface from given position of the source , the input aperture , function , “target” set , and output intensity . For example, the input intensity may have a “bell”-like shape and we may wish to redistribute the energy uniformly over a prespecified region. The analytical formulation of the described above problem leads to a non-linear partial differential equation of Monge-Ampère type. In our previous paper we proved existence of weak solutions to this inverse problem and in this paper we describe and illustrate with examples an algorithm for its numerical solution. The proposed numerical method can be easily modified for the case when is a closed domain on an arbitrary surface. Received November 26, 1996     

灰色实物型投入产出分析的覆盖解研究

由于国民经济系统的复杂性,人们在使用实物型投入产出分析工具时不可能获得各部门产品的投入与产出的确定值。采用灰色系统理论基本原理提出灰色实物型投入产出分析并给出模型及各种灰色分析系数的覆盖解公式。灰色实物型投入产出分析能处理统计数据为区间的情形,可以使决策者在不确定性情况下对复杂经济系统进行分析、预测和控制,提高人们的抗风险能力。模拟案例验证了模型计算的可行性。     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.