反問題中正則化方法的某些研究.pdf

1、大連理工大學(xué)碩士學(xué)位論文MASTERALDISSERTATIoN反問題中正則化方法的某些研究徐強(qiáng)學(xué)科、專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：羅鐘鉉教授論文答辯日期2005年12月18日笪堡!墾閨塑圭堊型垡查望塑苤些塹壅SomeResearchonRegularizationMethodinInverseProblemsAbstractAsanimportantclassofmathematicalphysicalproblems，inversepro

2、blemshavedevelopedintoapopularresearchdirectionSolvinganinverseproblemistodetermineunknowncausesbasedonobservationoftheireffectsNowadays，inverseproblemshavebeenusedinmanyfields，suchasinversemediumscattering，computerizedt

3、omography，etc，andthetheoryandmethodsarenovelandchallengingTwoessentialdifficultiesappearfrequentlyOneistheobservationdatapossiblydoesnotbelongtothecorrespondingsettotheexactsolution，anotheristhattheapproximationi8notstab

4、leThusinverseproblemsareoftenill—posed，andmostarenon—linearRegularizationtechniqueisa丑effectivemethodofsolvingflNposedinverseproblemsSinceregularizedparameterinfluencetheconvergentrate，whichbecomesmoreandmoreimportant，an

5、dthereareseveralsignificantresultsgottenbymanyresearchers，Basedonthemeritofcomputingglobalminimumwithhomotopycontinuationmethodin吼aposteriorregularizedhomotopycontinuationmethodispresentedinthisthesisRegularizedparameter

6、intheiterationisdecidedbyMorozovdiscrepancyprincipleWerealizedthecomputationininversemediumscatteringproblemswithmulti—experimentaldataoffarfieldpatternMoreover，theanalyticalresultofthattheselectedregularizedparameterine

7、achiterationaccordwithTikhonovregularizationtheoryfromafewofnumericalexperimentsisstatedThemethodofposteriorregularizedparametercanOVercometheshortcomingsofpriorchoose，andthenumericalexamplesshowthepracticabilityoiournew