简介：WediscussavariantofrestartedGMRESmethodthatallowschangesoftherestartingvectorateachcycleofiterations.Themeritofthevariantisthatpreviouslygeneratedinformationcanbeutilizedtoselectanewstartingvector,suchthattheoccurrenceofstagnationbemitigatedortheconvergencebeaccelerated.ThemoreappealingutilizationofthenewmethodisinconjunctionwithaharmonicRitzvectorasthestartingvector,whichisdiscussedindetail.Numericalexperimentsarecarriedouttodemonstratethattheproposedprocedurecaneffectivelymitigatetheoccurrenceofstagnationduetothepresenceofsmalleigenvaluesinmodulus.

简介：RecentlyY.Saadproposedaflexibleinner-outerpreconditionedGMRESalgorithmfornonsymmetriclinearsystems[4].Followingtheirideas,wesuggestanadaptivepreconditionedCGSmethod,calledCGS/GMRES(k),inwhichthepreconditionerisconstructedintheiterationstepofCGS,byseveralstepsofGMRES(k).Numericalexperimentsshowthattheresidualoftheouteriterationdecreasesrapidly.WealsofoundtheinterestingresidualbehaviourofGMRESfortheskewsymmetriclinearsystemAx=b,whichgivesaconvergenceresultforrestartedGMRES(k).Forconvenience,wediscussrealsystems.

简介：本文给出了重新启动的LGMRES方法的一种代价更小的实现方式。这种做法基于消除以下减慢收敛速度的现象：重新启动的simplerGMRES的每次循环结束时得到的残向量经常交替方向，与重新启动的GMRES的情形类似。这种新的变形的方法的优点是它比重新启动的LGMRES所需要的计算量要少，大量的例子表明该方法计算速度更快。

简介：Lagrangian-Eulerianformulationsbasedonageneralizedvariationalprincipleoffluid-solidcouplingdynamicsareestablishedtodescribeflow-inducedvibrationofastructureundersmalldeformationinanincompressibleviscousfluidflow.Thespatialdiscretizationoftheformulationsisbasedonthemulti-linearinterpolatingfunctionsbyusingthefiniteelementmethodforboththefluidandsolidstructures.Thegeneralizedtrapezoidalruleisusedtoobtainapparentlynon-symmetriclinearequationsinanincrementalformforthevariablesoftheflowandvibration.Thenonlinearconvectivetermandtimefactorsarecontainedinthenon-symmetriccoefficientmatrixoftheequations.Thegeneralizedminimumresidual(GMRES)methodisusedtosolvetheincrementalequations.AnewstablealgorithmofGMRES-Hughes-Newmarkisdevelopedtodealwiththeflow-inducedvibrationwithdynamicalfluid-structureinteractionincomplexgeometries.Goodagreementbetweenthesimulationsandlaboratorymeasurementsofthepressureandbladevibrationaccelerationsinahydroturbinepassagewasobtained,indicatingthattheGMRES-Hughes-Newmarkalgorithmpresentedinthispaperissuitablefordealingwiththeflow-inducedvibrationofstructuresundersmalldeformation.

简介：在分析GMRES-DR的基础上,将加权技术和GMRES-DR算法结合,从而加快GMRES-DR算法的收敛速度,并从理论上证明了加权GMRES-DR算法的每次循环生成仍是Krylov子空间,此外数值试验验证了该算法的有效性.

简介：GMRES方法是目前求解线性方程组使用较为广泛的方法。在分析GMRES方法的基础上，将加权技术和简单GMP．ES（m）算法结合，得到了加权简单GMRES（m）方法，并用数值试验验证了该算法的有效性。