模糊线性系统及广义特征值、奇异值问题

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1、华东师范大学博士后学位论文模糊线性系统及广义特征值、奇异值问题姓名：王珂申请学位级别：博士后专业：数学指导教师：陈果良20080601华东师范大学博士后研究工作报告AbstractFuzzymathematicshasmadearapidprogresssinceZadehfirstpresentedtheconceptoffuzzysetinthefoundationthesis‘‘FuzzySets”publishedin1965，andhasbeenregardedasaself-containedbranchofmathematics．Fuzzymathematic

2、shasmanyapplicationsinengineering，patternrecognition，imageprocessing，cyber-nation，economies，financeandSOon．Mostofthemmayboildowntofindingthesolutionoffuzzylinearsystemsintheend．ItrequiresUStoinvestigatethenumer-icalmethodsforsystemsoffuzzylinearequations．Whenthenumbersofvariablesbecomemuch

3、greater，iterativemethodswillbeconsideredasfirstchoices．Theperturbationanalysisalsoneedstobeconsidered．．Applicationsofthematrixgeneralizedeigenvalueproblemmostlyarisefromequationsofmathematicalphysics，statisticalanalysis，cybernation，linear-quadraticoptimalcontrolproblems，multi—bodysystems，a

4、rchitecture，bioscience，andSOon．Thesingularvalueandgeneralizedsingularvalueproblemshavesignificantapplica，．tionsinpatternrecognition，imageandsignalprocessing，statisticsandmanyotherareasofappliedmathematics．’Thereportpresentssomefurtherworkofblockiterativemethodsandpertur—bationanalysisforfu

5、zzylinearsystemsandthezero-structuredconditionnumbersforsingularvalue，generalizedeigenvalueandgeneralizedsingularvalue．First，westudytheblockiterativemethodsforfuzzylinearsystemwiththeiterativeschemesandtheconvergentconditions．Thenumericalexamplesshowthatthemethodsareeffectiveandpractical．S

6、econdly,theperturbationanalysisfornonsingularfuzzylinearsystemisbeenpresented．Theupperperturbationboundsarederived．Servalconditionnumbersaredefinedandtheirexplicitexpressionsareprovided．Finally,wediscussthezero-structuredconditionnumbersforsingularvalue，generalizedeigenvalueandgeneralizeds

7、ingularvalue。Wecandirectlycomputetheconditionnumberswiththeirexplicitexpressionstoestimatethesensitivityofasimplesingularvalue，generalizedeigenvalueandgeneralizedsingularvaluetozero-structuredperturbations．．111．AbstractKeywords：Fuzzylinearsystem；BlockSORmethod