奇異非線(xiàn)性方程組及非線(xiàn)性最小二乘問(wèn)題的求解.pdf

1、湘潭大學(xué)碩士學(xué)位論文奇異非線(xiàn)性方程組及非線(xiàn)性最小二乘問(wèn)題的求解姓名：楊柳申請(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：袁亞湘成央金20030401AbstractThepresentdissertationisconcernedwiththenumericalmethodsfornonlinearequationsandnonlinearleastsquareproblemsNumericalmethodsfornonlinearequat

2、ionsandnonlinearleastsquareproblemsareveryheatedresearchtopicsTheyhavewideapplicationsinchemicalengineering，aeromau—tics】mechanics，economyproductmanagement，communicationsandtrans—portations，etcLevenbergMarquardtmethodiso

3、neofthemostimportantmethodsforsolvingsystemsofnonlinearequationsRecentlyYamashitaandFukushima[4]showthatthesequenceproducedbytheLevenbergMarquardtmethodcon—vergesqnadraticllytothesolutionsetoftheequationsiftheparameteris

4、chosenasthequadraticnormofthefunctionandundertheweakerconditionthanthenonsingulaxitythatthefunctionprovidesalocalerrorboundnearthesolutionHowever，thequadratictermhassomeunsatisfactorypropertiesFanandYuan[61usesanothermet

5、hodthathasprovedunderthelocalerrorboundcondition，ifwechoicetheparameterasthenolnlofthefunction，thesequenceproducedbytheLevenbergMarquardtmethodconvergesquadrati—cllytoasolutionofthesystemoftheequationsHereweconsiderthech

6、oiceoftheparameterasthenormofthegratitudeofthefunctionWeproveun—derthelocalerrorboundconditionthattheLevenbergMarqUardtmethodwiththisparameterconvergesquadraticllytoasolutionofthesystemoftheequationsAndwealsopresenttwogl

7、oballyconvergentLevenbergMaxquardtalgorithmsusinglinesearchtechniquesandtrustregionapproachrespectivelyIna【ldtion，weintroducesomenewmethodsandtheoriesforsolvingsystemsofnonlinearleastsquareproblemsAnewLevenbergMarquardtm

8、ethodisproducedtosolvethehighdimemsionportfolioselectionmodelsweesxlsolvetheproblemquicklyandgetbetterresultsthanbeforeKeywords：nonlinearequations，localerrorbound，LevenbergMarquardtmethod，nonlinearleastsquareproblems，por