關于若干迭代算法的收斂性分析.pdf

1、浙江大學碩士學位論文關于若干迭代算法的收斂性分析姓名：李曉霞申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：韓丹夫20021201關于若干迭代算法的收斂性分析AbstractThealgorithmproblemofsolvingnonlinearoperatorequationY(x1=0inBanachspacehasbeenstudiededb5’manynumericalscientistsTheiterativemethodisam

2、ainalgorithmforsolvingnonlinearequationNow，theresearchofiterativemethodsbecomesthehardcoreofthesolutiontOallkindsofnonlinearproblemsWhethertilenonlinearproblemswillbesolvedwellornotisdirectlyaffectedbythechoiceofiterativ

3、emethods80itisveryimportantandmeaningfultodotheresearchofiterativemethodsThispaperconsistsoffivechapters，whichdiscussmainlyabouttheconvergenceofseveraliterativemethodsInChapter1，、、resummarizeseveraliterativemethodsandthe

4、irconvergencecondition，thetechniquesinprovingtheiterativemethods’SconvergencetheoremInChapter2，wepresentafamilyofiterativemethodwiththeconvergenceoforderthreeThefamilyofiterativemethodsavoidevaluatingthesecondFrechetderi

5、vati_、eInthisChapter，weestablishconvergencetheorembyusingthemajorizingmethodInChapter3thecorrectionofSuper—HalleyiterativemethodispresentedTheSuperHalleyiterativenmthodhasthethree—orderconvergence，butthecorrectionhasthef

6、our—orderInthisChapter，weestablishconvergencetheorembyusingtherecurrencerelationsInChapter4，theconvergenceoftheNewton—likeiterativemethodisgivenunderthenewconditionInChapter5，thedynamicsfortheiterativemethodsinChapters2a