一類非線性方程和非線性不等式問題的數值算法研究.pdf

1、福建師范大學碩士學位論文一類非線性方程和非線性不等式問題的數值算法研究姓名：余芝云申請學位級別：碩士專業(yè)：計算數學指導教師：馬昌鳳201106IIIIflllllllIIrlrlIII福建師范大學余芝云碩士學位論文Y1998406AbstractIllthisthesisthealgorithmsforsolvingsymmetricnonlme&requationsandnonlinearinequalitiesproblemsare

2、discl】胬edIIlchapterone，atrustregionbasedmodifiedNewtonmethodforsolving儼metricnonlinearequationsisstudiedAtfirst，thesymmetricnonlinearequations娥reformulatedasakindofunconstrainedoptimizationproblemThenthetrustregionbasedm

3、odifiedNewtonmethodispresentedforsolvingsymmetricnonlinearequationsInthisalgorithm，thesearchingdirectionbysolvingnonlinearequationsBesides，theiterationsequencesgeneratedbythisalgorithmareincludedinalevelsetwhichisbounded

4、ThesequencesgeneratedbythisalgorithmgloballyconvergetothesolutionofsymmetricnonlinearequationsundersomeadditionalassumptionsWhat’Smore，thisalgorithmhasthepropertyoflocalquadraticconvergenceTwoexamplesarequotedasthenumeri

5、calexampleswhicharecomputedunderdifferentdimensionsoftheproblemsincluding10，100，200，300，400and500withfivesetsofinitialvalues，whichpowerfullyillustratetheefficiencyofthealgorithmpresentedInchaptertwo，a11adaptivesimulateda

6、nnealingfloatingpointgeneticalgorithmforsolvingnonlinearinequalitiesproblemisstudiedAtfirst，thenonlinearinequalitiesproblemsarereformulatedasasetofnonsmoothingequations，thenbym她useofthesmoothingauxiliaryfunctiontheproble

7、mwasequallyconverted嬲thesmoothingunconstrainedoptimizationproblemsBasedonthistransformulation，theadaptivesimulatedannealingfloatingpointgeneticalgorithmispresented，whichnotonlypossestheglobalsearchingcapabilityofadaptive

8、simulatedannealingalgorithmandgeneticalgorithm，butalsomakeuptheshortageofgeneticalgorithmIntheend，thenumericalexperimentpowerfullyillustratetheefficiencyofthealgorithmpresentedInchapterthree，thewholethesisisgeneratedBesi

9、destheunsolvedproblemsinthisfieldandsomesuggestionsforOUrfurtherstudyarealsopointedoutKeywords：nonlinear，symmetricequations，inequalitiesproblems，trust—regionalgorithm，modifiedNewtonmethod，adaptivesimulatedannealing，float