Publication: Complexity Analysis of Automatic Differentiation in the Hyperion Software
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Complexity Analysis of Automatic Differentiation in the Hyperion Software

- incollection -
 

Author(s)
Josť Grimm

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
One important feature of the hyperion software is the rational approximation problem: given the m first terms of the power series expansion of a stable transfer function, find a stable approximation of it under the form P/q, of McMillan degree n. This leads to minimising ψ(Q), for some Q. In this chapter, we show different ways of computing ψ and its derivatives, and we indicate the complexity of these computations.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Grimm2002CAo,
       author = "Jos{\'e} Grimm",
       title = "Complexity Analysis of Automatic Differentiation in the Hyperion Software",
       pages = "305--310",
       chapter = "36",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "One important feature of the hyperion software is the rational approximation
         problem: given the $m$ first terms of the power series expansion of a stable transfer function, find
         a stable approximation of it under the form $P/q$, of McMillan degree $n$. This leads to minimising
         $\psi(Q)$, for some $Q$. In this chapter, we show different ways of computing $\psi$ and
         its derivatives, and we indicate the complexity of these computations."
}


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