大型線性方程組不完全分解預(yù)條件方法的研究.pdf

1、電子科技大學(xué)碩士學(xué)位論文大型線性方程組不完全分解預(yù)條件方法的研究姓名：周少博申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：黃廷祝20080501ABSTRABCTA。BSTRACTForthesparsematrixA，thepreconditionerwhichgeneratesfromcompletedecompositionusuallydoesnothavethesamesparseasthematrixA，generallymuc

2、hdenseSo，inordertogainthetwoendsthatpreconditionerkeepsparseandhavesufficienteffectincompletedecompositionapproachhasbeenproposedThepreconditionerthatcomesfromtheincompleteCholeskyfactorizationhasbeenshowntobeaveryeffect

3、ivepreconditionerforawidevarietyoflargesystemsoflinearequationsThepreconditionerLwhichisgeneratedformincompleteCholeskyfactorizationAlgorithm34inthispaperretainsthenumberofnonzeroofeachcolumnbetweennkandnkpThespecificnum

4、berofnonzeroelementswhichisretainedineachcolumnisdefinedbytheoptimalparameterfSo，thememoryofpreconditionerisconstrainedFromthenumericalexperimentitCallconcludethatitseemsthattheoptimalparameterfisthebestwhenitchoosesthec

5、ountdownoftheorderofmagnitudeoftheFrobeniusnormofthematrixandthatthenumberofPCGiterationofthenewalgorithminthispaperissameaSthenumberofPCGiterationofAlgorithm32ofLinandMor6，butthememoryislessthanAlgorithm32Fromtherelatio

6、nbetweenthemomentofsparsepatternSgeneratedandthewholeprocessofincompletefactorization，sparsepatternScallbedividedintotwocasesThefirstcaseisthestaticsparsepatternwhichisdeterminedpriortotheprocessoffactorization，thesecond

7、caseisthedynamicsparsepatternwhichCannotbepredeterminedisdeterminedduringthefactorizationForthesecondsparsepatternthispaperprovedthestabilitywhenthematrixAwhichistobebrokendownisasymmetricalM—matrixAtthesametime，fromthep