求解非线性方程组的LM方法

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1、万方数据V01．29(2009)No．3数学杂志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．andComputerScience，FujianNormalUniversity，Fuzhou350007，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．andwedenotebyX’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．万方数据254JournalofMathematicsV01．29dealswithunconstrainedequationsonly．Seealso[5，6]forsomesubsequentrelatedresultsfortheunconstrainedcase．Theorganizationofthispaperisasfollows：Inthenextsection．anL-Mmeth

8、odandsomeassumptionsareproposedforthesolutionofproblem(1．1)；thelocalsuperlinearandquadraticconve