求解非線性方程的若干非精確迭代法的收斂性分析.pdf

1、求解非線性方程的若干非精確迭代法的收斂性分析ConvergenceAnalysisofSeveralInexactIterativeMethodsforSolvingNonlinearEquations作者：肖媛Author：物anXiao指導教師：坌壹壅Supervisor：XiubinXu專業(yè)：計算數學學位o理學碩士授予單位：浙江師范大學Major：——Comp—u—ta—tiona—l————M——————a————t——h———

2、—e———m——————a———t———i——c———s——Degree：MasterofScienceInstitute：——ZhejiangNormalUniversityMay，2013AbstractTheproblemofsolvingnonhnearequationF(z)=0hasbeen831importantproblemofnumericalmathematicOneofthemostefficientalgorit

3、hmstosolvethisequationisiterativemethodInthisthesis，westudysemilocalconvergenceofinexactNewtonmethodunderweakconditions，andlocalconvergenceofinexactNewtonlikemethodsandinexactGanssNewtonlikemethodsundermajorantconditions

4、OurworkweakenssomerelevantconvergentconditionsandimprovessomeresultsThecontentsareasfollows：InChapter1，itpresentsthebackgroundandcurrentsituationforsolvingnonlinearequationsVariousvariantsofLipschitzconditionandtheassoci

5、atedresultsaresummarizedAlso；itintroducesrelevantdefinitionsandpreliminaryknowledge，suchasconvergenceorder，conditionofconvergenceandrelevantknowledgeinBanachspaceSomeoftheconceptsusedinthethesisarealsopresentedInChapter2

6、，undersomekindsofweakLipschitzconditions，anewsemilocalconvergenceanalysisforinexactNewtonmethodisobtainedbymajorizingsequenceanalysisUnifiedconvergencecriteriaensuringtheconvergenceareestablishedThisapproachalseachesanew

7、errorestimationandtheuniqueballofsolution，whichgeneralizetheexistingrelevantonesItisworthpointingoutthatapplicationstosomespecialcasessuchastheKantorovichtypeconditionsand7conditionsareprovidedandsomewellknownconvergence

8、theoremsforNewton’SmethodareobtainedascorollariesInChapter3，wedefinethecentermajorantconditionsAndundertheassumptionsthatFsatisfiesrelevantmajorantconditions，weestablishanewlocalconvergenceanalysisforinexactNewtonlikemet

9、hodandinexactGauss—NewtonlikemethodrespectivelyThisanalysissimplifiestheconditionsofconvergenceinrelevantreferencesandprovidesaclearrelationshipbetweenthemajorizingfunctionandthenonlinearoperatorParticularlytherelevantre