简介:TheJOURNALOFANCIENTCIVILIZATIONS(JAC)ispublishedannuallybytheInstitutefortheHistoryofAncientCivilizations(northeastnormaluniversity,Changchun,JilinProvince,People’sRepublicofChina).Thisyear,weareproudtopresentthe30thvolumetotheacademicaudience.Firstissuedin1986afterthefoundationof
简介:AmethodconstructinqC~1Piecewisequinticpolynomialoveratriangulargridtointerpo-latefunctionvaluesandpartialderivativesatverticesispresentedinthispaper.Thesetofprecisepoly-nomialsofthismethodisdiscussed.
简介:Afamilyofpiecewiserationalquinticinterpolationispresented.Eachinterpolationofthefamily,whichisidentifieduniquelybythevalueofaparameterαi,isofC2continuitywithoutsolvingasystemofconsistencyequationsforthederivativevaluesattheknots,andcanbeexpressedbythebasisfunctions.InterpolantisofO(hr)accuracywhenf(x)?Cr[a,b],andtheerrorshaveonlyasmallfloatingforabigchangeoftheparameterαi,itmeanstheinterpolationisstablefortheparameter.Theinterpolationcanpreservetheshapepropertiesofthegivendata,suchasmonotonicityandconvexity,andaproperchoiceofparameterαiisgiven.
简介:Inthispaper,weintroduceaconditionweakerthantheLpdifferentiability,whichwecallCpcondition.Weprovethatifafunctionsatisfiesthisconditionatapoint,thenthereexiststhebestlocalapproximationatthatpoint.WealsogiveanecessaryandsufficientconditionforthatafunctionbeLpdifferentiable.Inaddition,westudytheconvexityofthesetofclusterpointsofthenetofbestappoximationsoff,{Pe(f)}ase→0.