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

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...

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

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

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：<正>ItisprovedthateverylargeintegerN≡5（mod24）canbewrittenasN=p12+…+p52witheachprimepjsatisfying|pJ-（N/5|）1/2≤N11/23.ThisgivesashortintervalversionofHua’stheoremonthequadraticWaring-Goldbachproblem

简介：NearlyorthogonalLatinsquaresareusefulforconductingexperimentseliminatingheterogeneityintwodirectionsandusingdifferentinterventionseachateachlevel.Inthispaper,someconstructionsofmutuallynearlyorthogonalLatinsquaresareprovided.Itisprovedthatthereexist3MNOLS(2m)ifandonlyifm≥3ndthereexist4MNOLS(2m)ifandonlyifm≥4withsomepossibleexceptions.

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：TheLeastSquaresSupportVectorMachines(LS-SVM)isanimprovementtotheSVM.CombinedtheLS-SVMwiththeMulti-ResolutionAnalysis(MRA),thisletterproposestheMulti-resolutionLS-SVM(MLS-SVM).TheproposedalgorithmhasthesametheoreticalframeworkasMRAbutwithbetterapproximationability.AtafixedscaleMLS-SVMisaclassicalLS-SVM,butMLS-SVMcangraduallyapproximatethetargetfunctionatdifferentscales.Inexperiments,theMLS-SVMisusedfornonlinearsystemidentification,andachievesbetteridentificationaccuracy.

简介：

简介：Inthispaperwepresentanonmonotonetrustregionmethodfornonlinearleastsquaresproblemswithzero-residualandproveitsconvergenceproperties.Theextensivenumericalresultsarereportedwhichshowthatthenonmonotonetrustregionmethodisgenerallysuperiortotheusualtrustregionmethod.

简介：TwoLatinsquaresofordervarer-orthogonaliftheirsuperpositionproducesexactlyrdistinctorderedpairs.Thetwosquaresaresaidtober-orthogonalidempotentLatinsquaresanddenotedbyr-MOILS(v)iftheyareallidempotent.Inthispaper,weshowthatforanyintegerv≥28,thereexistsanr-MOILS(v)ifandonlyifr∈[v,v~2]\{v+1,v~2-1}.

简介：HASM(当模特儿的高精确性表面)技术基于表面的基本理论，它被证明了在表面适合改进插值精确性。然而，在以前的研究的不可分的反复的解决方案在计算和巨大的存储器用法导致了高时间的复杂性以便把这种技术放进申请变得困难，特别为大规模数据集。在学习，一个创新模型(HASM广告)根据数据调整理论根据顺序的最少的广场被开发。顺序的分割在这种技术被采用，以便线性方程能被划分成在顺序要处理，时间的复杂性在计算极大地减少了的组。实验显示HASM广告技术在精确性超过传统的空间插值方法。另外，交叉验证结果为土壤PH性质的空间插值证明一样的结论，数据在江西省取样了。而且，HASM广告技术显著地减少计算复杂性并且在计算减少记忆用法，这在学习被表明。

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

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