简介：在这篇论文，non-quasi-Newton“有用于非强迫的优化问题的不精确的线搜索的s家庭被学习。为non-quasi-Newton的一个新更改公式“sfamily被建议。如果，有任何一个Wolfe类型orArmijo类型线搜索的组成的算法全球性并且Q-superlinearly收敛，这被证明要最小化的功能hasLipschitz连续坡度。

简介：Inthispaper,wepresentasmoothingNewton-likemethodforsolvingnonlinearsystemsofequalitiesandinequalities.Byusingtheso-calledmaxfunction,wetransfertheinequalitiesintoasystemofsemismoothequalities.ThenasmoothingNewton-likemethodisproposedforsolvingthereformulatedsystem,whichonlyneedstosolveonesystemoflinearequationsandtoperformonelinesearchateachiteration.Theglobalandlocalquadraticconvergencearestudiedunderappropriateassumptions.Numericalexamplesshowthatthenewapproachiseffective.

简介：基于Thiele连分式，重新建立了求解非线性方程的经典的Newton迭代公式．为了避免求导数运算，采用差商可以近似代替导数的办法，得到Newton迭代方法的几个变体并给出了其收敛的阶数．最后，数值实例证实了这些迭代格式是有效的．

简介：Inthispaperweimprovethetwoversionsofthetwo-sidedprojectedquasi-Newtonmethod-onewasproposedbyNocedal&Overtonin[1]andtheotherwasdiscussedinourpreviouspaper,byintroducingthreedifferentmeritfunctionstomakeinexactone-dimensionalsearches.Itisshownthattheseimprovedquasi-Newtonalgorithmshavegainedglobalconvergencepropertywhichisnotpossessedbytheoriginaltwoalgorithms.

简介：TheHermitianandskew-Hermitiansplitting(HSS)methodisanunconditionallyconvergentiterationmethodforsolvinglargesparsenon-Hermitianpositivedefinitesystemoflinearequations.BymakinguseoftheHSSiterationastheinnersolverfortheNewtonmethod,weestablishaclassofNewton-HSSmethodsforsolvinglargesparsesystemsofnonlinearequationswithpositivedefiniteJacobianmatricesatthesolutionpoints.ForthisclassofinexactNewtonmethods,twotypesoflocalconvergencetheoremsareprovedunderproperconditions,andnumericalresultsaregiventoexaminetheirfeasibilityandeffectiveness.Inaddition,theadvantagesoftheNewton-HSSmethodsovertheNewton-USOR,theNewton-GMRESandtheNewton-GCGmethodsareshownthroughsolvingsystemsofnonlinearequationsarisingfromthefinitedifferencediscretizationofatwo-dimensionalconvection-diffusionequationperturbedbyanonlinearterm.ThenumericalimplementationsalsoshowthataspreconditionersfortheNewton-GMRESandtheNewton-GCGmethodstheHSSiterationoutperformstheUSORiterationinbothcomputingtimeanditerationstep.

简介：InthispaperwereportasparsetruncatedNewtonalgorithmforhandlinglarge-scalesimpleboundnonlinearconstrainedminimixationproblem.ThetruncatedNewtonmethodisusedtoupdatethevariableswithindicesoutsideoftheactiveset,whiletheprojectedgradientmethodisusedtoupdatetheactivevariables.Ateachiterativelevel,thesearchdirectionconsistsofthreeparts,oneofwhichisasubspacetruncatedNewtondirection,theothertwoaresubspacegradientandmodifiedgradientdirections.ThesubspacetruncatedNewtondirectionisobtainedbysolvingasparsesystemoflinearequations.Theglobalconvergenceandquadraticconvergencerateofthealgorithmareprovedandsomenumericaltestsaregiven.

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简介：符尚武等对二维三温能量方程提出了一种9点差分格式，它适用于任意三维网格。但他们用非线性块Gauss—Seidel方法求解所得的非线性代数方程组，收敛得非常慢且经常不得不因为迭代某些次数后仍不收敛而缩小时间步长。

简介：Fortheimprovedtwo-sidedprojectedquasi-Newtonalgorithms,whichwerepresentedinPartI,weproveinthispaperthattheyarelocallyone-steportwo-stepsuperlinearlyconvergent.Numericaltestsarereportedthereafter.ResultsbysolvingasetoftypicalproblemsselectedfromliteraturehavedemonstratedtheextremeimportanceofthesemodificationsinmakingNocedal&Overton’soriginalmethonpractical.Furthermore,theseresultsshowthattheimprovedalgoritnmsareverycompetitiveincomparisonwithsomehighlypraisedsequentialquadraticprogrammingmethods.

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简介：Aclassofperiodicinitialvalueproblemsfortwo-dimensionalNewton-Boussinesqequationsareinvestigatedinthispaper.TheNewton-Boussinesqequationsareturnedintotheequivalentintegralequations.Withiterationmethods,thelocalexistenceofthesolutionsisobtained.Usingthemethodofaprioriestimates,theglobalexistenceofthesolutionisproved.

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简介：有牛顿重复的一个新decoupled二系结算法为解决描述通过多孔的媒介过滤的液体流动的联合Navier-Stokes/Darcy模型被建议。而且错误估计被给，当时，它证明精确性的一样的顺序能作为在好网孔直接解决系统被完成h=H2。理论分析和数字实验为解决联合问题说明算法的效率。

简介：研究了一类奇异的非Newton多方渗流方程整体解存在性和渐进性.通过引进低能量函数的概念,证明了当初值u0(x)具有低能量时,其相应的解是整体存在的,且当t→∞时具有指数增长.

简介：Inthispaper,basedontheimplicitRunge-Kutta(IRK)methods,wederiveaclassofparallelschemethatcanbeimplementedontheparallelcomputerswithNs(Nisapositiveevennumber)processorsefficiently,anddiscusstheiterativelyB-convergenceoftheNewtoniterativeprocessforsolvingthealgebraicequationsofthescheme,secondlywepresentastrategyprovidinginitialvaluesparallellyfortheiterativeprocess.Finally,somenumericalresultsshowthatourparallelschemeishigherefficientasNisnotsolarge.