文档介绍：Chinuart小fa
2008,23550一564
OnDoubleRevisedNodesofSNBernstein
InterpolationProcessoftheThirdType
CH4NGMhbaob印BPing,YU4NXuegon
.Department司MatiematicsBaichengTeachersCollaeaicheng137000,
NathematicandJJormation8ciencnJontaiDnicersigntai204005Ching
AbatraetHntisworkthewelinownproblenpatprvardby5HBernstsinin1900
stadiediaadecpsep,Aoperatorsconstraciedbyreviingdoubleinterpoltionnodes
Itisprovedtiattheopertorconvegestoarbitrarycontinuousfunctonsanifornlyandtie
comvergenceorieristhebest
Keywordstinterpolationpoynonialanibracomergencethehighestcomergeaceorien
SNermstsiopmoblen
2000MRSabjectClessieationAI0
CLCamberOlfd4lDecumentcodeA
ArticleIDI0020462200901055906
81.,Introduction
WeallhnowthatLagrangeinterpolationpolynomialdoesnotconvergetoarbitarycontin
Mousfnetionsbniformiy,ToimprovettnilornconvergenceSNBernstsinllpatforvard
thefolowingquestionforgiving气刘andanarbiranycontingousunctiona英
荣posibletoconstructaninterpolationpokynomialwiththedegreeofMAB,训认eqaalto
J团吴Bven万pGintsand诊convergestojanilornlyshen万+
beinterestingihowtoconstructaninterpolationpolyomialsatisttingthe5NBermsteins
eqlirementmentionedasabovesothattheapproxdmationordersthebestWenamedthis
,Bemstsincorstructedaninterpolation
PobymomialandansweredtheaboweestionbuthisanswerisotthebestIn993ZhuLaiyi
studiedtheconvergenceorderftheinterpolationpomomiali