inane polynomial of degree Infully n sup norm in C lil 272 Tinkle Tnk any other

Inane polynomial of degree infully n sup norm in c

This preview shows page 46 - 55 out of 73 pages.

inanepolynomialofdegreeInfullynsupnorminClil2.72TinkleTnkanyothermonkpolynomialpCPn273Max1pct7XEC413EasytoAndzeroesandextremaofTnThWToSnOandOEOESTzeroesoddmultiplesof11722.75hmIcostIzjoan1extremeTnexItwhennojITjOnzitsXjcosJEjonnChebyshevpartsGausscobaltpointsT'acxj0jethIn1zeroesofTnandXoIXuI2.77TaahsinnoriggingxcosOthus2,7814t.CHsinnedInchDOhtt
butsinceSimcherOSinan1025150CosmoG79ThecxThICHF2Tactht 1Then280UnixTaytaySinai0sinceChebyshevpolynomialoftuesecondlandEEN3281queCxX1UniceThebyshevnodesarezeroesoffofcats
Chapter3interpolation3IPolynomialinterpolatrinpolynomialinterpolationproblemGivenntldatapointsXafoofCxnfnwhereEidistrictFindapolynomialpnenseenthatPnCXofopnexfiIgnterppdwathfryPnXnfnPointsXoXninterpdatmnodesvalvesfofefnfromdataorfunctionfofcofjfCxjj0hCetpnexgotaXtax'tanXrewriteinterpolationpropertygotaXotanxofoAotaXtanXfAotakntAnXpfhlinearsystemsrepresentinmathform
Notehomogenoussystemfj0jignhasonlythetrivialsolitonpmIoThenCBHhasauniquesolutionStartwithhL
n2mlifXo0ifxxXz0ExtendgalXXjxxjtxnxxxjXj1HjXjtDXjXnNITLXXiaKeocxgforjOnKejsatisfydjcxklfjo.ITpncxJloCx1fotliCHftalncxtfnIEoljcxsfjdjcxielementaryLagrangepolynomatotdgreenCallLatomal
theoremGwenhttvalvesGofocarfordistinctXoxnthereisauniquepolynomialpinofdegreeatmostngudrthetPnLxjfjforjOIhiProofiphisasolutionSupposeqnisanothersolutionGuelphqnCxjJfjfor50,1hTakerpngonrCRnrCxjpnexjqnlXjfjfjojojl.mnthusroThusqnpnThereforethesolutionisuniqueD3liquispacedandChebyshevNodesEIk7IIYaIIEbastteensuequiEksXjIcjhjoInhZNodesgoodtrigonometricpolynomialinterpolatebutnotfralgebraicpolynomialinterpolationlater
ChWaltoxcostJjanextremaofChebyshevpolynomialofdegreenClub9fromequirspacedpointsGeJainXcos0Notethatthesegofrom1toIToinsteadgo1to1oftendefinexjcosJohnNotequispaceddistenewendpointsoftheinterval32ConnectiontoBestomhnmApproximationGivenFECCarbbestuniformapproximatePintinPnischaracterizedbyenfpwhichequisosallatesatbeastat2timesThenenhasatleastnelzeroesSothereexistXoXusuchthatDidCtofewpnmxfoxPritam5fan
pPnbispolynomialofdegreeatnutonthatinterpolatesfatntlzeroesHardtofindpifromfindinghttinterpolationnodesQuestiongivenfoxesXnfamfrdistinctXooXninterpolatornodesinCabhowcloseispntheinterpolatingpolynomialofdegreeforfatthesenodestobestundomapproximatepinoffin1pm11PmPFHasNoticepnpeRninterpolatesfp3.16pnexpn.cxjajz.lyQfpCxDthenG17111PaBillaAnHfPfHaswheren13.18Anameaxxs.isgolljtlesbesgueConstantLeopardsoninterpolationnodesNotonf
3119Hfpallas11fpie

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture