Decomposition Algorithm For Linear Input-output Equations And Existentiality Results Of Nonlinear Input-output Equations

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.