Linear Programming and Extensions by George Dantzig PDF

By George Dantzig

ISBN-10: 0691080003

ISBN-13: 9780691080000

In real-world difficulties on the topic of finance, company, and administration, mathematicians and economists usually come upon optimization difficulties. First released in 1963, this vintage paintings appears to be like at a wealth of examples and develops linear programming equipment for recommendations. remedies lined comprise fee techniques, transportation difficulties, matrix tools, and the homes of convex units and linear vector areas.

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Get Linear Programming and Extensions PDF

In real-world difficulties concerning finance, company, and administration, mathematicians and economists usually come upon optimization difficulties. First released in 1963, this vintage paintings seems at a wealth of examples and develops linear programming tools for ideas. remedies coated contain cost innovations, transportation difficulties, matrix tools, and the houses of convex units and linear vector areas.

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3) asymptotisch stabil sein. 5) muS deshalb Wurzeln Iz;l < 1, i = 1,2, ... , m besitzen. FaSt man nun die zeitvarianten Parameter 0 eines Prozesses als ZustandsgroBen auf, dann kann als Parameterzustandsmodell des Prozesses geschrieben werden + 1) = IO(k) + ,,(k) y(k + 1) = ",T(k + I)O(k) + n(k + 1) . 7) Hierbei beschreibt ,,(k) eine (deterministische) Parameteranderung. 1 oben angegeben. 4 in Form eines vektoriellen Markov-Prozesses bzw. eines Random-walk-Prozesses angesetzt. Der rekursive LS-Parameterschatzalgorithmus lautet nach Gl.

GI. 23). Der Unterschied dieser zweistufigen Methode zur einstufigen Methode der kleinsten Quadrate nach Kap. 8 besteht darin, daB die Ausgangswerte vor der Parameterschatzung gemittelt werden und somit eine erste Verminderung des Storsignaleinflusses erreicht wird. AuBerdem wird dadurch das Biasproblem bei korreliertem Fehlersignal umgangen. )y(k) . 2) Die Korrelationsfunktionen konnen dabei auch rekursiv ermittelt werden. 3) wobei fur die Gewichtung der neuen MeBwerte auch noch andere Moglichkeiten bestehen.

Es wird ferner fiir einen ProzeB zweiter Ordnung dargestellt, daB mit zunehmendem Storsignal/Nutzsignal-Verhaltnis Un/Uy,. fiir die Varianzen gilt: - var [Ali j ] ist zunachst proportional zu (Un/Uyu)2 und strebt dann gegen einen festen Wert (ab etwa un/uyu ~ 2) - var [AbJ nimmt proportional zu (U n/Uyu)2 zu - var [Aej ] und var [Adj ] (Storsignalfilter) sind naherungsweise unabhangig von un/uy,.. Siehe auch Eykhoff (1974), S. 259. 4 Zusammenfassung Die Maximum-Likelihood-Methode geht aus einer statistischen Betrachtungsweise der beobachteten Signale hervor.

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Linear Programming and Extensions by George Dantzig


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