解非对称线性系统的混合bicr法

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1、广西大学硕士学位论文(2010)解非对称线性系统的混舍BiCR法manynumericalexperiments，CGSshowsgoodperformance，however，itoftenhasirreg-ularandoscillatoryconvergencebehaviorsf8，171．ManynumericalexperimentsshowthatBiCGSTABiSfasteranditsconvergencebehavioriSmoresmooththanCGS『18，271．BasedontheBiCGSTA

2、B，M．H．GutknechtproposedBiCGSTAB2f151thatisexplainedasthecombinationofBiCGandGMRES(2)『91．G．L．G．SleijpenandD．R．FokkemaproposedBiCGSTAB(L)『181thatisexplainedasthecombinationofBiCGandGMRES(L)『9，121．However，thechoiceofLisdifficultforsolvingrealisticproblems．Astheextension

3、ofCRmethod，Bi-ConjugateResidual(BiCR)methodproposedby【19，26】hasbeenreportedthatresidualnormtendstoconvergefasterandoscillationissmallerthantheBiCGmethod【271．BasedontheBiCRmethod，andmotivatedbythetechniqueofhybridBiCGmethod，weproposehybridBiCRmethod．Wewillgiveanunifie

4、dwaytoderiveaclassofhybridBiCRmethods．AndbYintroducingathree-termrecurrencepolynomial．ahybridBiCRmethodisproposed，wecallitGeneralizedhybridBiCRmethod(GhBCR)．PrehminarynumericalexperimentsshowthatOurhybridBiCRmethodssl'eeffectiveinmanysituations．Thispaperisorganizedas

5、follows：inthenextchapter，wewillintroducerelevantpre-hminaries，involvingsomebasicdefinitions，KrylovsubspacemethodandbiconjugateA-orthogonalization．Inchapter3，hybridBiCRmethodisproposed．Thederivationoftherecurrencecoefficientsandconstructionofstandardpolynomialwillbegi

6、ven．Withthestandardpolynomial，aGeneralizedhybridBiCRmethod(GhBCR)willbegiven．TheconclusionwiUbegiveninchapter4．2广西大学硕士学位论文(20lO)解非对称线性系统的混合BiCR法Chapter2．Preliminaries2．1．Somebasicdefinitions【2】2(1)Innerproduct：Ifa，b∈／T'，thentheinnerproduct(a，b)ofaandbhas：(a，b)=∑：1bia

7、i．Propertiesofinnerproduct：(a，b)=(b，a)；(a+b，c)=(n，c)+(b，c)，whereC∈舻；(ka，b)=k(a，6)，where七∈R．(2)Symmetricmatrix：IfCisthetranspositionofmatrixA，thenC=AT令勺=％．IfmatrixAissymmetric，thenA=AT；IfmatrixAisnonsymmetric，thenA≠AT．(3)Subspace：Givevectorsal，⋯，an∈舻，thesetofalllinear

8、combinationsofthevectorsnl，⋯，anisasubspaceexplainedasthespan{al，⋯，on)，flspan{al，⋯，凸n)={∑j=1％％：％∈R】．(4)Independence：Ifasetofvectors{