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

简介：Order-recursiveleast-squares(ORLS)algorithmsareappliedtotheprob-lemsofestimationandidentificationofFIRorARMAsystemparameterswhereafixedsetofinputsignalsamplesisavailableandthedesiredorderoftheunderlyingmodelisunknown.Onthebasisofseveraluniversalformulaeforupdatingnonsymmetricprojec-tionoperators,thispaperpresentsthreekindsofLSalgorithms,callednonsymmetric,symmetricandsquarerootnormalizedfastORLSalgorithms,respectively.Astotheau-thors’knowledge,thefirstandthethirdhavenotbeensofarprovided,andthesecondisoneofthosewhichhavethelowestcomputationalrequirement.Severalsimplifiedversionsofthealgorithmsarealsoconsidered.

简介：与计算力量的开发，在那里，数据试穿的一个增加的焦点被联系了为高保真度的地震倒置技术地震速度模型和图象，例如完整波形的倒置和最少的广场移植。尽管更多比常规方法进展了，这些数据试穿方法不管多么能以计算费用是很昂贵的。最近，优化这些数据试穿的各种各样的技术地震倒置问题被实现了迎合对很改进的效率的工业需要。在这研究，我们建议一个将军随机为这些数据试穿结合坡度方法相关反的问题。我们首先规定我们的方法的基本理论然后给合成例子。我们的数字实验为大尺寸的地震倒置申请说明这个方法的潜力。

简介：这篇文章的目的是为不可压缩的magnetohydrodynamic方程开发并且分析最少平方的近似。最少平方的有限元素方法的主要优点是它不受到所谓的Ladyzhenskaya相当於Mr或Sir的称谓?ka-Brezzi(LBB)状况。作者采用包含与在H-1的内部产品有关的一个分离内部产品的最少平方的functionals(蠅)。

简介：Inthispaper,wepresenttheleast-squaresmixedfiniteelementmethodandinvestigatesuperconvergencephenomenaforthesecondorderellipticboundary-valueproblemsovertriangulations.OnthebasisoftheL2-projectionandsomemixedfiniteelementprojections,weobtainthesuperconvergenceresultofleast-squaresmixedfiniteelementsolutions.ThiserrorestimateindicatesanaccuracyofO(h3/2)ifthelowestorderRaviart-Thomaselementsareemployed.

简介：我们开发并且分析一个一阶的系统最少平方光谱为秒顺序的方法有可变系数的椭圆形的边界价值问题。我们首先分析theChebyshev加权的标准最少平方功能由L_ω~2-1)-norm和H_ω~的和定义(方程然后我们代替的剩余的-1)-norm由分离否定标准和分析的否定标准分离Chebyshev加权的最少平方的方法。光谱集中为建议方法被导出。我们也介绍各种各样的数字实验。Legendreweighted最少平方的方法能被跟随这篇论文容易开发。

简介：Inthispaper,least-squaxesmirrorsymmetricsolutionformatrixequations(AX=B,XC=D)anditsoptimalapproximationisconsidered.Withspecialexpressionofmirrorsymmetricmatrices,ageneralrepresentationofsolutionfortheleast-squaresproblemisobtained.Inaddition,theoptimalapproximatesolutionandsomealgorithmstoobtaintheoptimalapproximationareprovided.

简介：我们在场一个方法基于为崎岖地形学的有飞机波浪编码的最少平方的反向的时间移植(P-LSRTM)。而不是在移植前修改波浪领域，我们修改编码函数的飞机波浪并且在模型在崎岖地形学上面充满经常的速度到区域以便P-LSRTM能直接以对射击的域颠倒时间移植一样的方法从崎岖表面被执行。为了改进效率和还原剂I/O(输入／输出)费用，动态编码策略和混血儿，编码策略被实现。在P-LSRTM能压制的SEG崎岖地形学模型表演的数字测试在迁居的迁居人工制品想象，并且高效地在中间深的部分补偿振幅。没有数据修正，P-LSRTM能生产一幅令人满意的图象近表面如果我们能得到精确近表面的速度，当模特儿。而且，预先叠PLSRTM面对迁居速度错误是比常规请读使用手册更柔韧的。

简介：张肌正规分解(是的shortedCANDECOMP/PARAFAC或CP)作为等级一个张肌的和分解张肌，它在信号处理发现众多的应用，hypergraph分析，数据分析，等等。轮流出现最少平方(ALS)是为解决它的最流行的数字算法之一。当为提高它的效率有大量努力时，一般来说，它的集中不能被保证。在这份报纸，我们合作从优化的ALS和信任区域技术回答产生轮流出现的trust-region-based最少平方(TRALS)为CP的方法。在温和假设下面，我们证明TRALS产生的整个反复的顺序收敛到CP的一个静止的点。这因此提供一个合理方法减轻沼泽地，ALS的臭名昭著的现象减慢算法的速度。而且，信任区域本身，与轮流出现的规则化相对照最少平方(RALS)方法，在选择参数提供一个自我适应的方法，它为算法的效率是必要的。我们的理论结果因此是比RALS在的强壮的[26]，它仅仅证明RALS产生的反复的顺序的簇点是一个静止的点。以便加速新算法，我们采用一个推测计划。我们从chemometrics，BCM分解和等级把我们的算法用于氨基酸荧光数据分解--(Lr，Lr，1)分解从信号处理产生，并且把它与ALS和RALS作比较。数字结果证明TRALS比ALS和RALS优异，两个从重复和中央处理器的数字预定观点。

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

简介：Nonlinearstochasticoptimalcontrolproblemsarefundamentalincontroltheory.Ageneralclassofsuchproblemscanbereducedtocomputingtheprincipaleigenfunctionofalinearoperator.Here,wedescribeanewmethodforfindingthiseigenfunctionusingamovingleast-squaresfunctionapproximation.Weuseefficientiterativesolversthatdonotrequirematrixfactorization,therebyallowingustohandlelargenumbersofbasisfunctions.Thebasesareevaluatedatcollocationstatesthatchangeoveriterati...

简介：Inthispapertheleast-squaresmixedfiniteelementisconsideredforsolvingsecondorderellipticproblemsintwodimensionaldomains.Theprimarysolutionuandthefluxerareapproximatedusingfiniteelementspacesconsistingofpiecewisepolynomialsofdegreekandrrespectively.Basedoninterpolationoperatorsandanauxiliaryprojection,superconvergentH^1-errorestimatesofboththeprimarysolutionapproximationuhandthefluxapproximationσhareobtainedunderthestandardquasi-uniformassumptiononfiniteelementpartition.ThesuperconvergenceindicatesanaccuracyofO(h^r+2)fortheleast-squaresmixedfiniteelementapproximationifRaviart-ThomasorBrezzi-DouglasFortin-MarinielementsoforderrareemployedwithoptimalerrorestimateofO(h^r+l).

简介：Uponusingthedenotativetheoremofanti-HermitiangeneralizedHamiltonianmatrices,wesolveeffectivelytheleast-squaresproblemmin‖AX-B‖overanti-HermitiangeneralizedHamiltonianmatrices.WederivesomenecessaryandsufficientconditionsforsolvabilityoftheproblemandanexpressionforgeneralsolutionofthematrixequationAX=B.Inaddition,wealsoobtaintheexpressionforthesolutionofarelevantoptimalapproximateproblem.

简介：获得更高精确的位置估计，随机的模型被估计由用观察的剩余，，因此随机的模型更写实地在大小描述噪音和偏爱。由使用GPS数据和广播位置推算历，在亚米水平显示精确位置估计的数字结果是可获得的。

简介：在这份报纸，一个一阶的椭圆形的系统管理的一个抑制分布式的最佳的控制问题被考虑。最少平方的混合有限元素方法，不易于Ladyzhenkaya-Babuska-Brezzi一致性条件，被用于与二个未知州的变量解决椭圆形的系统。由更多样地采用Lagrange，途径，包括一个最初的州的方程的连续、分离的optimality系统，一个伴随状态方程，和为最佳的控制的变化不平等分别地被导出。分离州的方程和分离伴随状态方程产出一个对称、积极的明确的线性代数学的系统。因此，象preconditioned那样的流行解答者结合坡度(PCG)，代数学的多格子(AMG)能被用于快速的答案。最佳一个priori错误估计分别地，在H在H1()-norm,并且为流动状态和伴随流动状态为原来的状态和伴随状态在L2()-norm,为控制函数被获得(div；)标准。最后，我们使用一个数字例子验证理论调查结果。[从作者抽象]

简介：Thispaperpresentsanewhighlyparallelalgorithmforcomputingtheminimum-normleast-squaressolutionofinconsistentlinearequationsAx=b(A∈Rm×n,b∈R(A)).Bythisalgorithmthesolutionx=A+bisobtainedinT=n(log2m+log2(n-r+1)+5)+log2m+1stepswithP=mnprocessorswhenm×2(n-1)andwithP=2n(n-1)processorsotherwise.

简介：Inphysicalmodeltestsforhighlyreflectivestructures,oneoftenencountersaproblemofmultiplereflectionsbetweenthereflectivestructuresandthewavemaker.Absorbingwavemakerscancancelthere-reflectivewavesbyadjustingthepaddlemotion.Inthispaper,weproposeamethodtodesignthecontrollerofthe2-Dabsorbingwavemakersysteminthewaveflume.Basedonthefirst-orderwavemakertheory,afrequencydomainabsorptiontransferfunctionisderived.Itstimerealizationcanbeobtainedbydesigninganinfiniteimpulseresponse(IIR)digitalfilter,whichisexpectedtoapproximatetheabsorptiontransferfunctionintheleastsquaressense.AcommonlyusedapproachtodeterminetheparametersoftheIIRfilterisapplyingtheTaylorexpansiontolinearizethefilterformulationandsolvingthelinearleast-squaresproblem.However,theresultisnotoptimalbecausethelinearizationchangestheoriginalobjectivefunction.Toimprovetheapproximationperformance,weproposeaniterativereweightedleast-squares(IRLS)algorithmanddemonstratethatwiththefiltersdesignedbythisalgorithm,theapproximationerrorscanbereduced.Physicalexperimentsarecarriedoutwiththedesignedcontroller.Theresultsshowthatthesystemperformswellforbothregularandirregularwaves.

简介：Arealn×nsymmetricmatrixX=(x_(ij))_(n×n)iscalledabisymmetricmatrixifx_(ij)=x_(n+1-j,n+1-i).Basedontheprojectiontheorem,thecanonicalcorrelationde-compositionandthegeneralizedsingularvaluedecomposition,amethodusefulforfindingtheleast-squaressolutionsofthematrixequationA~TXA=Boverbisymmetricmatricesisproposed.Theexpressionoftheleast-squaressolutionsisgiven.Moreover,inthecorrespondingsolutionset,theoptimalapproximatesolutiontoagivenmatrixisalsoderived.Anumericalalgorithmforfindingtheoptimalapproximatesolutionisalsodescribed.

简介：Biasofring-laser-gyroscope(RLG)changeswithtemperatureinanonlinearway.ThisisanimportantrestrainingfactorforimprovingtheaccuracyofRLG.Consideringthelimitationsofleast-squaresregressionandneuralnetwork,weproposeanewmethodoftemperaturecompensationofRLGbiasbuildingfunctionregressionmodelusingleast-squaressupportvectormachine(LS-SVM).StaticanddynamictemperatureexperimentsofRLGbiasarecarriedouttovalidatetheeffectivenessoftheproposedmethod.Moreover,thetraditionalleast-squaresregressionmethodiscomparedwiththeLS-SVM-basedmethod.TheresultsshowthemaximumerrorofRLGbiasdropsbyalmosttwoordersofmagnitudeafterstatictemperaturecompensation,whilebiasstabilityofRLGimprovesbyoneorderofmagnitudeafterdynamictemperaturecompensation.Thus,theproposedmethodreducestheinfluenceoftemperaturevariationonthebiasoftheRLGeffectivelyandimprovestheaccuracyofthegyroscopeconsiderably.