弱條件下解非線性方程算法的收斂性.pdf

1、哈爾濱理工大學碩士學位論文弱條件下解非線性方程算法的收斂性姓名：劉甲好申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：潘狀元20090301哈爾濱理工大學理學碩士學位論文TheConvergenceofAlgorithmforSolvingNonlinearEquationsUnderWeakConditionAbstractIterativemethodsareveryimportantalgorithmtothenumericalsolu

2、tionforsolvingnonlinearequations，thechosenofadvantageordisadvantageiterativemethodseffectsderectlythegoodorbadresultofnonlinearequtions，theresearchofgooditerativemethodsforsolvingnonlinearequationsareveryimportantandnece

3、ssarySeekinglesscomputational，highermoreefficientiterativemethodsandconstructingnewcriterionsofconvergenceforiteratvemethodsarealwaysfocusedbymanynumericalanalysisresearchers，theproblemshavebecametopicalissuesInthisartic

4、letheresearchquestionsforsolvingnonlinearequationsarefocusedsomeiterativemethodsatestudiedunderweakcondition，theconvergenceoftheseiterativemethodsareanalysedtheoretically碭Pcontentofthispaperisasfollows：Theachievementsofn

5、umericalsolutionofnonlinearequationsareanalysedandsummarizedathomeandabroad，thesignificanceandpracticalbackgroundofsolvingnonlinearequationsareexpoundedunderweakconditionandthemaincontentofthearticleareintroducedinthepre

6、faceBymeansofSmale’Spointestimatesandthemajorantmethod，theconvergenceofSecantmethodforsolvingthenonlinearequtionsisstudiedandprovedunderweakconditionColumnupdateBroydenmethodforsolvingnonlinearequationsisstudiedunderweak

7、conditionandtheexistenceandconvergencetheoremi8alsogiven；columnupdateBroydenmethodcankeepthesparsitywhentheequationsaresparse，andthecomputationofthismethodismoreeasyWepresentafamilyofiterativemethodwiththeconvergenceofor