By G. Baron (auth.), Edmund Hlawka, Robert F. Tichy (eds.)
This quantity includes unique examine papers provided at a seminar given on the Technical college of Vienna. participants mentioned tools drawn initially from quantity concept yet utilized now to numerical research, discrete arithmetic and theoretical machine technological know-how.
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Extra resources for Number-Theoretic Analysis: Seminar, Vienna 1988-89
Sample text
The G-differential of Eq. 1) is obtained by applying the definition given in Eq. 8) to each row in Eq. 1). For example, the G-differential of the i th row of Eq. 1) is ( ∂ u 0j + εhu j d N 0 0 aij U + εhU ,α + εhα dε j =1 ∂t ∑ ( ( 0 ) 0 + bij U + εhU ,α + εhα ) ( ∂ u 0j + εhu j ∂x )− c (U i ) 0 + εhU ,α 0 + εhα = 0. 12) and ( ) ∑ ∂∂cα(e ) − ∑ ∂a∂α(e ) ∂∂ut S i e 0 ; hα = I i 0 0 m m =1 N 0 ik 0 k 0 m k =1 + ( ) ∂bik e 0 ∂u k0 hα . 13) ∂α m0 ∂ x m In view of Eq.
Furthermore, the Adjoint Sensitivity System is linear in the adjoint function. In particular, for linear problems, the Adjoint Sensitivity System is independent of the original state-variables, which means that it can be solved independently of the original system. In summary, the ASAP is the most efficient method to use for sensitivity analysis of systems in which the number of parameters exceeds the number of responses under consideration. It is important to emphasize that the “propagation of moments” equations are used both for processing experimental data obtained from indirect measurements and also for performing statistical analysis of computational models.
As discussed in Volume I of this book, the scope of both the FSAP and the ASAP is to calculate exactly and efficiently the local sensitivities of the system’s response to variations in the system’s parameters, around their nominal values. The FSAP constitutes a generalization of the decoupled direct method (DDM), since the concept of Gâteaux-differential (which underlies the FSAP) constitutes Copyright © 2005 Taylor & Francis Group, LLC 28 Sensitivity and Uncertainty Analysis the generalization of the concept of total-differential in the calculus sense, which underlies the DDM.