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(xué)碩士學(xué)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(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：潘狀元20090301哈爾濱理工大學(xué)理學(xué)碩士學(xué)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