简介：Considersolvinganoverdeterminedsystemoflinearalgebraicequationsbyboththeleastsquaresmethod(LS)andthetotalleastsquaresmethod(TLS).Extensivepublishedcomputationalevidenceshowsthatwhentheoriginalsystemisconsistent.oneoftenobtainsmoreaccuratesolutionsbyusingtheTLSmethodratherthantheLSmethod.ThesenumericalobservationscontrastwithexistinganalyticperturbationtheoriesfortheLSandTLSmethodswhichshowthattheupperboundsfortheLSsolutionarealwayssmallerthanthecorrespondingupperboundsfortheTLSsolutions.InthispaperwederiveanewupperboundfortheTLSsolutionandindicatewhentheTLSmethodcanbemoreaccuratethantheLSmethod.Manyappliedproblemsinsignalprocessingleadtooverdeterminedsystemsoflinearequationswherethematrixandrighthandsidearedeterminedbytheexperimentalobservations(usuallyintheformofalimeseries).Itoftenhappensthatasthenumberofcolumnsofthematrixbecomeslarger,thera

简介：LetGbeasimplegraphwithnverticesandλn（G）betheleasteigenvalueofG.Inthispaper,weshowthat,ifGisconnectedbutnotcomplete,thenλn（G）≤λn(Kn-11)andtheequalityholdsifandonlyifGKn-11,whereKn-11,isthegraphobtainedbythecoalescenceofacompletegraphKn-1ofn-1verticeswithapathP2oflengthoneofitsvertices.

简介：Datafittingisanextensivelyemployedmodelingtoolingeometricdesign.Withtheadventofthebigdataera,thedatasetstobefittedaremadelargerandlarger,leadingtomoreandmoreleast-squaresfittingsystemswithsingularcoefficientmatrices.LSPIA(least-squaresprogressiveiterativeapproximation)isanefficientiterativemethodfortheleast-squaresfitting.However,theconvergenceofLSPIAforthesingularleast-squaresfittingsystemsremainsasanopenproblem.Inthispaper,theauthorsshowedthatLSPIAforthesingularleast-squaresfittingsystemsisconvergent.Moreover,inaspecialcase,LSPIAconvergestotheMoore-Penrose(M-P)pseudo-inversesolutiontotheleast-squaresfittingresultofthedataset.ThispropertymakesLSPIA,aniterativemethodwithcleargeometricmeanings,robustingeometricmodelingapplications.Inaddition,theauthorsdiscussedsomeimplementationdetailofLSPIA,andpresentedanexampletovalidatetheconvergenceofLSPIAforthesingularleast-squaresfittingsystems.

简介：1.IntroductionThepurposeofthispaperistostudytheleastsquaresproblemofthematrixequationF~PGwithrespecttoPcSa,i.e.(PI)R\qIIF--PGll,whereF,GERnxmandG/0.Where11’11denotestheFrobeniusnorm,andSa~{XeS'fX20},S'={XER'''IX=X'}.Problem(PI)wasfirstformulatedbyAll...

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简介：Inthispaperthenewnotionofmultivariateleast-squaresorthogonalpoly-nomialsfromtherectangularformisintroduced.Theirexistenceanduniquenessisstudiedandsomemethodsfortheirrecursivecomputationaregiven.Asanapplica-isconstructed.

简介：AnegativecurvaturemethodisappliedtononlinearleastsquaresproblemswithindefiniteHessianapproximationmatrices.Withthespecialstructureofthemethod,anewswitchisproposedtoformahybridmethod.Numericalexperimentsshowthatthismethodisfeasibleandeffectiveforzero-residual,small-residualandlarge-residualproblems.

简介：Thispaperdiscussespointwiseerrorestimatesfortheapproximationbyboundedlinearoperatorsofcontinuousfunctionsdefinedoncompactmetricspaces(X,d),Theauthorsintroduceanewmajorautofthemodulusofthecontinuitywhichisthesrnallestamongthoseg(ξ)'swhichhavethefollowingpropertiesω(f，ε)≤9(f，ε)andg(f,λε)≤(1+λ)g(f,ε)andbythismajorantanewquantitativeKorovkintypetheoremonanycompactmetricspaceisproved.

简介：一张签署的图是一张图，一个符号属于每个边。这篇论文从图扩大拉普拉斯算符矩阵的一些基本概念到签署的图。Inparticular，在最少的拉普拉斯算符特征值之间的关系和一张签署的图的失衡的海角被调查。

简介：Inthispaper,wepresentsomeiterativemethodsforsolvinglthorderautoregressivemodels,proveglobalconvergenceforl=1case,andthenumericalresultsofnewalgorithmsseemtobemoreefficientthantheonesofCochrane-Orcuttiterativemethod.

简介：TheGalerkinandleast-squaresmethodsaretwoclassesofthemostpopularKrylovsubspacemethOdsforsolvinglargelinearsystemsofequations.Unfortunately,boththemethodsmaysufferfromseriousbreakdownsofthesametype:InabreakdownsituationtheGalerkinmethodisunabletocalculateanapproximatesolution,whiletheleast-squaresmethod,althoughdoesnotreallybreakdown,isunsucessfulinreducingthenormofitsresidual.Inthispaperwefrstestablishaunifiedtheoremwhichgivesarelationshipbetweenbreakdownsinthetwometh-ods.Wefurtherillustratetheoreticallyandexperimentallythatifthecoefficientmatrixofalienarsystemisofhighdefectivenesswiththeassociatedeigenvalueslessthan1,thentherestart-edGalerkinandleast-squaresmethodswillbeingreatrisksofcompletebreakdowns.Itappearsthatourfindingsmayhelptounderstandphenomenaobservedpracticallyandtoderivetreat-mentsforbreakdownsofthistype.

简介：Weproveconvergenceforameshfreefirst-ordersystemleastsquares(FOSLS)partitionofunityfiniteelementmethod(PUFEM).Essentially,byvirtueofthepartitionofunity,localapproximationgivesrisetoglobalapproximationinH(div)∩H(curl).TheFOSLSformulationyieldslocalaposteriorierrorestimatestoguidethejudiciousallotmentofnewdegreesoffreedomtoenrichtheinitialpointsetinameshfreedis-cretization.Preliminarynumericalresultsareprovidedandremainingchallengesarediscussed.

简介：Physicalactivity(PA)isaneffectivemeansofcurbingtheprevalenceofchildobesity,andfundamentalskillsarehypothesizedtobeanimportantfactorthatdeterminesphysicallyactiveorinactivebehaviorinchildren.Researchevidencesuggeststhatadolescentsandyoungadultswithproficientmotorskillsinsport-relatedactivitiesaremorelikelytohaveaphysicallyactivelifestyle.1Becausephysically

简介：最少的广场LS时间延期评价是一个古典、有效的方法。然而，表演由于矩阵inversing的不稳定性在信号噪音SNR的低比率的情形严重地被降级。以便解决这个问题，装载最少的广场DL-LS的对角线被把一个积极明确的矩阵加到反的矩阵建议。而且，修理斜装载的缺点从规则化的点被分析当低SNR的忍耐被增加时，诚实被减少。这个问题被再装解决。主要评价相互作为斜装载被介绍，它导致在到达并且在另外的时间的更大的装载的时候的小斜装载。模拟和水池实验证明算法有更好的性能。

简介：SeveralARMAmodelingapproachesareaddressed.Inthesemethodsonlypartofacorrelationsequenceisemployedforestimatingparameters.Itissatisfying,ifthegivencorrelationsequenceisofrealARMA,sinceanARMAprocesscanbecompletelydeterminedbypartofitscorrelationse-quence.Butforthecaseofameasuredcorrelationsequencethewholesequencemaybeusedtore-ducetheeffectoferroronmodelparameterestimation.Inaddition,thesemethodsnowdonotguar-anteeanonnegativespectralestimate.Inviewoftheabove-mentionedfact,aconstrainedleastsquaresfittingtechniqueisproposedwhichutilizesthewholemeasuredcorrelationsequenceandguar-anteesanonnegativespectralestimate.

简介：半的答案性质参量的模型被分析，特别，最不惩罚了那为半摆平参量的模型当矩阵B~TPB是ill-posedor时，将无效单个。根据为线性参量的模型的山脉估计的原则，为半概括了惩罚最少的广场参量的模型被提出，并且一些公式和估计的统计性质被导出。最后，根据模拟例子，一些有用结论被得出。

简介：增加的算法是过去常改进回归分析的一般性能的一般方法的一个类。主要想法是在火车集合上维持分布。以便直接使用给定的分发，一请修改了算法被建议并且用作基础学习者处理非线性多变量回归问题。Experimentson汽油辛烷数字预言表明那增加请修改了算法在PLS算法上有更好一般的性能。

简介：LetMbeacompactorientable3-manifoldwithMconnected.IfV∪SWisaHeegaardsplittingofMwithdistanceatleast6,thenthe-stabilizationofV∪SWalongMisunstabilized.HenceMhasatleasttwounstabilizedHeegaardsplittingswithdifferentgenera.ThebasictoolisaresultondiskcomplexgivenbyMasurandSchleimer.

简介：LetG=(V(G),E(G))beasimpleconnectedgraphofordern.Foranyverticesu,v,w∈V(G)withuv∈E(G)anduw∈E(G),anedge-rotatingofGmeansrotatingtheedgeuv(aroundu)tothenon-edgepositionuw.Inthiswork,weconsiderhowtheleasteigenvalueofagraphperturbswhenthegraphisperformedbyrotatinganedgefromtheshorterhangingpathtothelongerone.

简介：Byusingthenon-parametricleastsquaremethod,thestrongconsistentestimationsofdistributionfunctionandfailurefunctionareestablished,wherethedistributionfunctionF(x)afterlogisttransformationisassumedtobeapproximatedbyapolynomial.Theperformanceofsimulationshowsthattheestimationsarehighlysatisfactory.