PDF-SIAMJ.COMPUT.Vol.6,No.2,June1977FASTPATTERNMATCHINGINSTRINGS*DONALDE.K

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324DONALDEKNUTHJtIVIESHMORRISJRANDVAUGHANRPRATIWeshallfirstconsiderthealgorithminaconceptuallysimplebutsomewhatinefficientformSections3and4ofthispaperdiscusssomewaystoimprovetheefficiencyand

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SIAMJ.COMPUT.Vol.6,No.2,June1977FASTPATTERNMATCHINGINSTRINGS*DONALDE.K: Transcript

324DONALDEKNUTHJtIVIESHMORRISJRANDVAUGHANRPRATIWeshallfirstconsiderthealgorithminaconceptuallysimplebutsomewhatinefficientformSections3and4ofthispaperdiscusssomewaystoimprovetheefficiencyand. C ONTROL PTIM 2002SocietyforIndustrialandAppliedMathematics Vol41No3pp954974 Abstract An averaging technique for nonlinear multiscale singularly perturbed control systems is developed Issues concerning the existence and structure of limit occupationa Abstract. 1.Introductionandmotivations.Thelast12yearshavewitnessedmanycontributionstotheinpaintingproblemindigitalimages,i.e.,theproblemofrecoveringentireregions 1144F.CAO,Y.GOUSSEAU,S.MASNOU,ANDP.PER Abstract.Withdiscretizedparticlevelocityspace,amulti-scaleuniedgas-kineticschemeforentireKnudsennumberowshasbeenconstructedbasedonthekineticmodelinone-dimensionalcase[J.Comput.Phys.,vol.229(2010),pp STRONGROTUNDITYANDOPTIMIZATION147integralfunctionalonL1,withdomainsomesubsetofthepositivecone;typicallyfwillhavenosubgradientsatzoounless,attheveryleast,zooisalmosteverywherestrictlypositive.Thusstron SPHERICALSPLINEAPPROXIMATIONDuetothisspecialrepresentation,manypropertiesofSBBpolynomialsareanal-ogoustothoseofclassicalplanarBernstein ReceivedbytheeditorsMarch17,2005;acceptedforpublication(inrevisedform)July6,2006;publishedelectronicallyJanuary12,2007.http://www.siam.org/journals/sinum/45-1/62708.html J.QIAN,Y.-T.ZHANG,ANDH.-K.ZHAO ACCELERATIONOFSTOCHASTICAPPROXIMATION839Toobtainthesequenceofestimates(t)tlofthesolutionx*of(1),thefollowingrecursivealgorithmwillbeused:XtXt-YtYtYtAxt-b+t,lt-1(2)2,7i=0EXi-Xoisanarbitrary(nonrandom)p 708GIRARDMEURANTprovedthattheinverseistridiagonal(thisisAsplund'sresult)andconversely.In1973,BukhbergerandEmel'yanenko[11]gaveformulasbasedonCholeskyfactorizationfortheinverseofasymmetrictridiagonalma HOWFASTARENONSYMMETRICMATRIXITERATIONS?779TABLEIterativemethodsfornonsymmetricsystemsAxb.(Thedifferencesamongthesealgorithmsareslightinsomecases.)Theterminologyap-proximatelyfollowsElman[6]andGutknech 1002U.FEIGE,RRAGHAVAN,D.PELEG,ANDE.UPFAL"Xi"Xj,"andgivesthewronganswerwithsomeprobability.Eachleafislabeledwithapermutationrepresentingthesortedorderfortheinput(forsortingandmerging)oranindexin[1,N](f ThisworkissupportedbyNSFunderGrantCCF-0702662. J.Comput.Sci.&Technol.,Month200X,Vol.21,No.X Figure1:Left:typesofgeometricerrors.Middle:apolygonsoupthatexhibitsamixtureofgeometricerrors.Right:atopologi supportedG55-97-1-0318andDMS-9804985andG-1-2070andNAS1-97046whiletheauthorwasinresidenceatICASE,NASALangleyResearchCenter,Hampton,23681-2199,andAFOSRgrantF49620-99-1-0077. troductionInrecenhighorderum 2(x+2)�2x�"1 4"x2+"�4 4�"x"�1 2(2�x)"x2InFigure6weshowtheinterpolationofdegree6ofthesolutionu"correspondingto"=0.5withthepoint0notrepeated,repeatedonceandtwice,re 3CorrespondingauthorFigure1OurmodelPISEallowstotransfernewposeortexturetoasinglepersonimageandalsoenablesregioneditingitisdif2culttopredictasharpandreasonableimagewithsparsecorrespondenceswhenthesourc

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