兩類解非線性方程f(x)=0的高階迭代法.pdf

1、蘭州大學(xué)碩士學(xué)位論文兩類解非線性方程f（x）=0的高階迭代法姓名：張玉新申請學(xué)位級別：碩士專業(yè)：數(shù)學(xué)計算數(shù)學(xué)指導(dǎo)教師：張國鳳20090501蘭州大學(xué)碩士學(xué)位論文AbstractWiththedevelopmentofscientifictechnologyandelectriccomputeroneofthemostimportantandchallengingproblemsinscientificandengineeringappl

2、icationsistofindthesolutionsofthenonlinearequationsThenonlinearfiniteelementproblem，thebound—aryvalueproblemsappearinginKinetictheoryofgases，elasticityandotherappliedareasarereducedtosolvingtheseequationsManyoptimization

3、problemsalsoleadtosuchequationsThispaperisconcemedwiththehighorderiterativemethodsforfindingasimpleroot％ie。，，(7)=0andf7()≠0off(x)=0，wheref：R_冗，bethecontinuouslydifferentiablerealfunctionThispaperisdividedintofourchapters

4、：Infirstchapter，theactualbackgroundofthisproblemismainlyintroduced，andthedevelopmentsituationofthisproblemisrecollected，thensomeelementaryknowledgeisoutlinedInsecondchapterafamilyofseventhorderiterativemethodsforsolvingn

5、onlinearequationf(x1=0ispresentedandanalyzedThisfamilyofseventh—ordermethodscontainstheBi’Sseventhordermethods【10】andmanyotherseventh—orderiterativemethodsasspecialcasesIntermsofcompu—tationalcost，periterationthenewmetho

6、dsrequirethreeevaluationsofthefunctionandoneevaluationofitsfirstderivative，thereforetheirefficiencyindexis1627Theconvergenceofthisfamilyofmethodsisanalyzedtoestablishitsseventh—orderconvergenceNumericalcomparisonsaremade

7、withseveralotherexistingmethodstOshowtheperformangeofthepresentedmethodsInthirdchapterafamilyofneweighthorderiterativemethodsforsolvingnonlinearequationf(x)=0arepresentedandanalyzedThenewmethodsarebasedonKou’Sseventhorde

8、rmethods[5】Intermsofcomputationalcost，periterationthenewmethodsrequirethreeevaluationsofthefunctionandoneevaluationofitsfirstderivative，thereforetheirefficiencyindexis1682Theconvergenceofthenewiterativemethodsisanalyzedt

9、oestablishtheireighth—orderconvergenceSeveralexam—piesaregiventoillustratetheefficiencyandtheperformanceofthenewmethodsFinallyweextendthepresentmethodstothegeneralmulti—stepiterativemethodandobtainanewfamilyofmultistepit