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1、萬(wàn)方數(shù)據(jù)V01．29(2009)No．3數(shù)學(xué)雜志J．ofMath．(PRC)ONL—MMETHoDFORNONLINEAREQUATIONS。JIANGLi—hual，MAChang-fengr2·3(1．Dept．ofMath．&Physics，AnhuiUniversityofScience&Technology．Huainan232001，China)(2．Dept．ofComputationalScience&Math．，GuilinInstituteofElectronicTechnology。Guilin541004，Chin
2、a)(3．CollegeofMath．a(chǎn)ndComputerScience，F(xiàn)ujianNormalUniversity，F(xiàn)uzhou350007，China)Abstract：Inthispaper，weconsidertheconvergenceL-Mmethodforsolvingasystemofsingularnonlinearequations．ThroughselectinganewparameterandgivinganewL-Mmethod．weshowthelocalsuperlinearandquadraticalc
3、onvergenceofthesequencegeneratedbythenewL-Mmethod。Numericalexperimentsshowthatthemethodperformsbetterforsingularproblems．Keywords：nonlinearequationsIlocalerrorboundlL-Mmethod2000MRSubjectClassificationl90(233I65K10DocumentcodelAArticleID：0255．7797(2009)03．0253—101Introduc
4、tiOnConsiderthenonlinearequationsF(z)=0WhereF：R“·R“isacontinuallydifferentiablefunctionthroughoutthisthatthesolutionsetof(1．1)benonempty．a(chǎn)ndwedenotebyX’thesetofTheauthorsdescribealgorithmsthathavecertainglobalandlocal(1．1)paper’weassumesolutionto(1．1)．fastconvergenceprope
5、rtiesunderanonsingularassumptionatthesolution，see[1，2，3]．Thenonsingularassumptionimpliesthatthesolutionislocalunique．Here，wepresentanL_Mmethodthatislocallyquadraticallyconvergentunderaweakerassumptionthat，inparticular，allowsthesolutionsettothelocallynounique．Tothisend，wer
6、eplacethenosingularityassumptionbyanerrorboundcondition．ThisismotivatedbytherecentpaperE4-]that*Receiveddate：2006·10—30Accepteddate：2007-06-30Foundationitem：Supportedbythemaster．doctorFoundationandtheyouthFoundationofAnhuiUniversityofScience＆Technology．Biography：JiangLihu
7、a(1979-)，feale。bornatHuaiyuan，Anhui．Master．majorinNumericalOptimization．萬(wàn)方數(shù)據(jù)254JournalofMathematicsV01．29dealswithunconstrainedequationsonly．Seealso[5，6]forsomesubsequentrelatedresultsfortheunconstrainedcase．Theorganizationofthispaperisasfollows：Inthenextsection．a(chǎn)nL-Mmeth
8、odandsomeassumptionsareproposedforthesolutionofproblem(1．1)；thelocalsuperlinearandquadraticconve
