A rank 1 SDP approach for the sensor network localization problem [Elektronische Ressource] / vorgelegt von Ania López

Ania Lopez

Description

)"*2.9. )"!"#$'(%%-!$.9.&'(< )#)*+",0)&-:)2&"23.+*/%.0)1%.2*3?@@A045%.!"62**)&*34.B !"5,#6*+#$%/$6%&'()$%'(*"+45""$6#7.8)$,7..$8$.$,-,"(*(!(E#$.)0/$*,$01,*2/$*,.*+(@)0/$*,$01,*2C'..$$."*(3(A.78B45""$6#7.8?'("+9$#.!+#$.:(A.58!,;@%*($."*(3(#?$8$.$,$A.78B.>67.*',9$,$)%*;!,;D#$.(@&'()$%'(*"+4.B)0<'(!.=*""$,"+!()'8(6*+)$:)$,';>%':!6(3()$,#$.FGBFGBGHHI/$*,.*+)"!%) !"#$(%),%&'&'&01*'!(&*%)*)'&&*%#&*/.%#')%&*!*$2+'&),#3)**&,&*%/'!)*%-')&.#')4,nmin{C•X |A(X) =b, X ∈S },+nX ∈Sm n m nn b∈R A :S →R C∈SnS+n nn S := {M ∈ S | S 0} C•X+C Xn nXXC•X =tr(CX) = C X .ij iji=1 j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

Sujets

• Mathematics

Informations

• Publié par: heinrich-heine-universitat_dusseldorf
• Publié le: 01 janvier 2008
• Nombre de lectures: 22
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

67.*',9$,$)%*;!,;D#$.(@&'()$%'(*"+4.B)0%':!6(3()$,#$.FGBFGBGHHI/$*,.*+)"!%) !"#$(%),%&'&'&01*'!(&*%)*)'&&*%#&*/.%#')%&*!*$2+'&),#3)**&,&*%/'!)*%-')&.#')4,nmin{C•X |A(X) =b, X ∈S },+nX ∈Sm n m nn b∈R A :S →R C∈SnS+n nn S := {M ∈ S | S 0} C•X+C Xn nXXC•X =tr(CX) = C X .ij iji=1 j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nmin{C•X |A(X) =b, X ∈S },+
nX ∈S
m n m nn b∈R A :S →R C∈S
nS+
n nn S := {M ∈ S | S 0} C•X+
C X
n nXX
C•X =tr(CX) = C X .ij ij
i=1 j=1
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nmin{C•X |A(X) =b, X ∈S },+
nX ∈ S
mn b∈R
n m nA : S → R C ∈ S
nS+
n nn S :={M ∈S |S 0} C•X+
C X
n nXX
C•X =tr(CX) = C X .ij ij
i=1 j=1
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