用新的加速迭代格式求解奇異問(wèn)題.pdf

1、哈爾濱理工大學(xué)碩士學(xué)位論文用新的加速迭代格式求解奇異問(wèn)題姓名：王穎申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)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NewAccelerationIterativeMethodsforSingularProblemsAbstractManyequationsarisinginpracticalapplicationaresingularnonlinearequations，suchassadd

2、lepoints，bifurcationpointsandfoldpointsereSostudyingthenumericalmethodofsolvesingularproblemshasveryimportantpracticalmeaningMostiterativemethodsarewellstudiedfornonsingularproblems，SOtheresearchforsolvingsingularproblem

3、sisacomplementarytothenonlineartheoryDeckerKelley，HBKellerhavestudiedNewtonmethod，ChordmethodandQuasiNewtonmethodforsolvingsingularnonlinearequations，theconvergencetheoremisprovedandtheasymptoticrateofconvergenceisobtain

4、edWithoutadditionalcalculations，multi—stepiterativemethodsareconstructedforsolvingsingularnonlinearproblemsbyspacegeometrypropertiesinthispaper，thebetterasymptoticconvergenceratesareobtained’Severalnumericalmethodsforsin

5、gularnonlinearequationsarestudiedinthispaper，themainresultsareasfollows：First，theoriginalmethodiSimproved，newaccelerationiterativeschemeiSconstructed，itsconvergencetheoremisprovedandtheestimationoftheconvergencerateisgiv

6、enSecond，foraclassofnonlinearsingularequationsinR一，arow。column‘updateQuasiNwetonmethodisgiventheiterativesequenceconvergestox，themethodkeepssparsityandsymmetryThesufficientconditionsofconvergencearegivenandtheconvergence