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

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：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.

简介：Inthispaperwepresentanonmonotonetrustregionmethodfornonlinearleastsquaresproblemswithzero-residualandproveitsconvergenceproperties.Theextensivenumericalresultsarereportedwhichshowthatthenonmonotonetrustregionmethodisgenerallysuperiortotheusualtrustregionmethod.

简介：为相对主要的积极整数u0并且r，并且为0kn，定义uk:=u0+kr。让Ln:=最小公倍数(u0，u1，...，un)并且让一，2是的l任何整数。在这份报纸，作者显示出那，为整数一，r最大(一，l1)并且nlr，下列不平等抓住$$L_n\geqslantu_0r^{\left({l-1}\right)\alpha+一-l}\left({r+1}\right)^n.$$特别地，让3产出的l=Ln上的以前的更低的界限在2010由hong和Kominers获得了的最好上的改进。

简介：Thefollwingsituationinusingthemethodofleastsquarestosolveproblemsoftenoccurs.Aftermexperimentscompletedandasolutionofleastsquaresobtained,the(m+1)-thexperimentismadefurtherinordertoimprovetheresults.Amethodofalgebraicoperationofspecialmatricesinvoledintheproblemisgivenisthispaperforobtaininganewsolutionforthem+1experimentsbasedupontheoldsolutionfortheprimarymexperiments.Thismethodisvalidformoregeneralmatrices.

简介：WeextendtheobliqueprojectionmethodgivenbyY.Saadtosolvethegeneralizedleastsquaresproblem.Thecorrespondingobliqueprojectionoperatorispresentedandtheconvergencetheoremsareproved.SomenecessaryandsufficientconditionsforcomputingthesolutionortheminimumN-normsolutionofthemin||Ax-b||M2havebeenproposedaswell.

简介：这份报纸为感动一般水准(PARMA)模特儿的原因、可颠倒的周期的autoregressive调查加权的最不绝对的偏差评估者(WLADE)。评估者的Asymptotic规度在一个部分时刻条件下面被导出。模拟研究被给估计建议WLADE的表演。

简介：WepresentcomponentwiseconditionnumbersfortheproblemsofMoorePenrosegeneralizedmatrixinversionandlinearleastsquares.Also,theconditionnumbersfortheseconditionnumbersaregiven.

简介：Analgorithmforsolvingnonlinearleastsquaresproblemswithgenerallinearinequalityconstraintsisdescribed.Ateachstep,theproblemisreducedtoanunconstrainedlinearleastsquaresprobleminasubspacedefinedbytheactiveconstraints,whichissolvedusingthequasi-Newtonmethod.ThemajorupdateformulaissimilartotheonegivenbyDennis,GayandWelsch(1981).Inthispaper,westatethedetailedimplementofthealgorithm,suchasthechoiceofactiveset,thesolutionofsubproblemandtheavoidanceofzigzagging.Wealsoprovethegloballyconvergentpropertyofthealgorithm.

简介：AbstractIntheparametertrackingoftime-varyingsystems,theordinarymethodisweightedleastsquareswiththerectangularwindowortheexponentialwindow.Inthispaperweproposeanewkindofslidingwindowcalledthemultipleexponentialwindow,andthenuseittofittime-varyingGaussianvectorautoregressivemodels.Theasymptoticbiasandcovarianceoftheestimatoroftheparameterfortime-invariantmodelsarealsoderived.Simulationresultsshowthatthemultipleexponentialwindowshavebetterparametertrackingeffectthanrectangularwindowsandexponentialones.

简介：有自我地图f的n周期的点的数字的二代数学的更低的界限：一个协议的MM变光滑尺寸歧管至少3：NF<潜水艇class=“a-plus-plus”>n(f)=min{#Fix(g<啜class=“a-plus-plus”>n)；gf；g是连续的}并且NJD<潜水艇class=“a-plus-plus”>n(f)=min{#Fix(g<啜class=“a-plus-plus”>n)；gf；g是光滑的}。一般来说，NJD<潜水艇class=“a-plus-plus”>n(f)可能比NF大得多<潜水艇class=“a-plus-plus”>n(f)。如果M是一个花托，那么，invariants是相等的。我们证明为一个nonabelian协议谎言组的一张自我地图，与自由的基本的组一起，平等保持f导致的商cohomology同形的所有特征值有moduli1。