30898.關于不可導方程或導數(shù)不可逆方程的迭代法的收斂性分析

1、關于不可導方程或導數(shù)不可逆方程的迭代法的收斂性分析ConvergAnal3“ofIterationMhodsononvergenceAnalysisofIterationethodS0nMNondifferentiableorDerivativeIrreversibleEquations作者：詹銅霞Author：墜望豎i墾圣塾塑指導教4坌壹塾Supervisor：XiubinXu專業(yè)：計算數(shù)學Major：——Computat——i——o

2、nalM—a—t—h—ema——t———i———c————s—————學位：墨堂塑Degree：Master旦墮cience授予單位o浙江師范大學Institute：——ZhejiangNormalUniversity——May2014AbstractUsingiterativealgorithmstosolvenonlinearequationF(x)=0isnotonlyanim—portantmathematicalproblem

3、，butalsohavingawiderangeofpracticalapplicationsinengineering，economicsandotherdisciplinesThisthesismainlyconcernstheconvergenceofgeneralizedNewtonmethodandGaussNewtonmethodexploringtheapproximatesolutionofF(x)=0Ourworkwe

4、akenssomerelevantconvergenceconditionsandimprovessomeresultsThecontentsareasfollows：Chapter1introducesthebackgroundandcurrentsituationoftraditionaliterationsAlso，itpresentsrelevantpreliminaryknowledge，suchaspatternofiter

5、ation，conditionofconvergence，B—subdifferentialandrelevantknowledgeinBanachspaceSomeoftheconceptsusedinthethesisarealsopresentedInChapter2，whensolvingnonlinearequationF(x)=0，ifthederivativeofF(x)doesn’texist，wedivideFinto

6、differentiablepartandnondifferentiablepartByusinganymatrixfromtheB—subdifferentialofthenondifferentiableterm，wepresentanewgeneralizedNewtonmethodandobtainitslocalconvergenceandsemilocalconvergenceunderW—conditionThemaint

7、heoremsobtainedinthissectionextendsomeresultsof[10，34]InChapter3，weuseGauss—Newtonmethodtoexploretheapproximatesolutionofp(x)=0whenthederivativeofFisnotinvertibleBylettingFsatisfyamajorantconditionandacentermajorantcondi

8、tionatthesametime，weobtainitslocalconvergenceThemaintheoremsobtainedinthissectionexpandtherangeofconvergenceandimprovetheresultsof[33]Keywords：GeneralizedNewtonMethods；B—subdifferential；LocalConvergence；SemilocalConverge