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1、IterativeMethodsforLargeLinearSystemsHenkA.vanderVorstMathematicalInstituteUtrechtUniversityUtrecht,TheNetherlandsvorst@math.uu.nlc2000byH.A.vanderVorst.AllRightsReserved.June24,20022Contents1Introduction71.1Ontheoriginofiterativemethods...............81.2Argumentsforiterativemethods
2、................141.3AnExample............................161.4Performanceaspects.......................182BasicIterationMethods212.1Introduction............................212.2TheKrylovsubspaceapproach.................252.3TheKrylovsubspace.......................272.3.1Amoreaccurat
3、ebasisfortheKrylovsubspace....303Constructionofapproximatesolutions333.1TheRitz-Galerkinapproach...................333.2Theminimumresidualapproach................343.3ThePetrov-Galerkinapproach.................353.4Theminimumerrorapproach..................364TheConjugateGradientsmeth
4、od394.1Computationalnotes.......................434.2TheconvergenceofConjugateGradients............494.2.1Locale?ectsintheconvergencebehavior.......524.3ParallelismanddatalocalityinCG...............574.4ParallelperformanceofCG...................624.4.1Processorcon?gurationanddatadist
5、ribution.....634.4.2RequiredCommunication................634.5CGandtheNormalEquations.................654.6Furtherreferences........................7135GMRESandMINRES735.1GMRES..............................735.2MINRES.............................795.3Rank-oneupdatesfortheMatrixSplitt
6、ing...........815.4GMRESRandGMRES?.....................866Bi-ConjugateGradients896.1Derivationofthemethod....................896.2AnotherderivationofBi-CG..................916.3QMR...............................936.4CGS................................957Howseriousisirregularconvergen
7、ce?1017.1Reliableupdating.........................1037.2Roundingerrorsanddiscretizationerrors...........1067.3E?ectsofroundingerrorstoKrylovprocesses.........1077.3.1TheLanczosrecurrencein?niteprecision.......1107.3.2E?ectsofroundingerrorsonimplementations.....1147.3.3Someconsiderati
8、onsforCG....
