【作者】 方恒；

【导师】 刘颖范；

【作者基本信息】 南京邮电大学 ， 应用数学， 2011， 硕士

【摘要】 基于经典(矩阵型)投入产出分析,本文首先考虑经典的投入产出方程。为此,将矩阵分析中的矩阵分解,优化理论以及算法等方法应用于投入产出方程,从而得到相关的近似解。进而研究一类非线性连续型条件Leontief投入产出方程,其主要可解性问题由存在性与连续性组成。对此,应用ky-Fan零点存在定理,并采用从特殊到一般的思想,得到了关于这类方程的可解性结果,并给出了相关的经济意义。全文共分六个章节:第一章,简要的概述了投入产出分析模型的产生和发展,回顾了经典的投入产出方程与非线性投入产出分析的研究现状。第二章,应用广义逆矩阵方法对经典和外贸型投入产出方程进行求解,并用matlab语言进行实例计算。第三章,当经典或外贸型投入产出矩阵是对称正定矩阵时,相关的投入产出方程被考虑并用共轭梯度法进行处理。第四章,引入了基于Galerkin原理的GMERS算法,并应用它们对于经典和外贸型投入产出方程。第五章,研究了一类非线性投入产出方程,应用Ky-Fan零点存在定理和集值映射方法获得了包含存在性与连续性的可解性结果。第六章,回顾了本文研究的一些方法和结果,展示了一些尚待解决的问题。更多还原

【Abstract】 Based on the classical (matrix type) input-output analysis, the classical input-outputequations are first considered. To this end, applying the matrix decomposition methods,optimization theory and associated algorithms in matrix analysis, the correspondingapproximatesolutionsareobtained.Then a class of nonlinear continuous type conditional Leontief input-output equation isconsidered, and the main solvabilityproblems composed of existence andcontinuityare studied.Byapplyingtheky-Fanzeroexistencetheorem,andusingtheideafromparticulartogeneral,thesolvability results with respect to this equation are gotten, and also, the relevant economicsignificanceareprovided.Thispaperisdividedintosixsections.:In the first chapter, a brief emergence and development regarding the input-output modelarereviewedfortheclassicalinput-outputequationandthenonlinearinput-outputanalysis.In the second chapter, the classical and the foreign-trade-type input-output equations aresolvedwiththegeneralizedinversematrixapproach,andcalculatedwiththematlablanguage.When the classic or the foreign-trade-type input-output matrix is symmetric positivedefinite,thecorrespondinginput-outputequationsareconsideredinChapterIII, andtackledbytheconjugategradientmethod.In Chapter IV, the Gmers algorithm based on Galerkin principle is introduced, and areappliedtodealwiththeclassicalandforeign-trade-typeinput-outputequations.A class of nonlinear input-output equation is studied in Chapter V, and the correspondingsolvability results composed of existience and continuity are obtained by applying Ky-Fancriticalpointtheoremandtheset-valuedanalysismethod.In the final chapter, the methods and results in this article are reviewed, and someunsolvedproblemsarealsopresented.更多还原