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：Theoptimallyweightedleastsquaresestimateandthelinearminimumvarianceestimatearetwoofthemostpopularestimationmethodsforalinearmodel.Inthispaper,theauthorsmakeacomprehensivediscussionabouttherelationshipbetweenthetwoestimates.Firstly,theauthorsconsidertheclassicallinearmodelinwhichthecoefficientmatrixofthelinearmodelisdeterministic,andthenecessaryandsufficientconditionforequivalenceofthetwoestimatesisderived.Moreover,undercertainconditionsonvariancematrixinvertibility,thetwoestimatescanbeidenticalprovidedthattheyusethesameaprioriinformationoftheparameterbeingestimated.Secondly,theauthorsconsiderthelinearmodelwithrandomcoefficientmatrixwhichiscalledtheextendedlinearmodel;undercertainconditionsonvariancematrixinvertibility,itisprovedthattheformeroutperformsthelatterwhenusingthesameaprioriinformationoftheparameter.

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

简介：Thispaperdevelopsgoalprogrammingalgorithmtosolveatypeofleastabsolutevalue(LAV)problem.Firstly,wesimplifythesimplexalgorithmbyprovingtheexistenceofsolutionsoftheproblem.Then,wepresentagoalprogrammingalgorithmonthebasisoftheoriginaltechniques.TheoreticalanalysisandnumericalresultsindicatethatthenewmethodcontainsalowernumberofdeviationvariablesandconsumeslesscomputationaltimeascomparedtocurrentLAVmethods.

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