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Structure and Efficient Jacobian Calculation

- incollection -
 

Author(s)
Thomas F. Coleman , Arun Verma

Published in
Computational Differentiation: Techniques, Applications, and Tools

Editor(s)
Martin Berz, Christian Bischof, George Corliss, Andreas Griewank

Year
1996

Publisher
SIAM

Abstract
Many computational tasks require the determination of the Jacobian matrix, at a given argument, for a large nonlinear system of equations. Calculation or approximation of a Newton step is a related task. The development of robust automatic differentiation (ad) software allows for ``painless″ and accurate calculation of these quantities; however, straightforward application of ad software on large-scale problems can require an inordinate amount of computation. Fortunately, large-scale systems of nonlinear equations typically exhibit either sparsity or structure in their Jacobian matrices. In this paper, we proffer general approaches for exploiting sparsity and structure to yield efficient ways to determine Jacobian matrices (and Newton steps) via automatic differentiation.

Cross-References
Berz1996CDT

AD Theory and Techniques
Sparsity

BibTeX
@INCOLLECTION{
         Coleman1996SaE,
       author = "Thomas F. Coleman and Arun Verma",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "Structure and Efficient {J}acobian Calculation",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "149--159",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Coleman1996SaE",
       crossref = "Berz1996CDT",
       abstract = "Many computational tasks require the determination of the Jacobian matrix, at a
         given argument, for a large nonlinear system of equations. Calculation or approximation of a Newton
         step is a related task. The development of robust automatic differentiation (AD) software allows for
         ``painless'' and accurate calculation of these quantities; however, straightforward
         application of AD software on large-scale problems can require an inordinate amount of computation.
         Fortunately, large-scale systems of nonlinear equations typically exhibit either sparsity or
         structure in their Jacobian matrices. In this paper, we proffer general approaches for exploiting
         sparsity and structure to yield efficient ways to determine Jacobian matrices (and Newton steps) via
         automatic differentiation.",
       keywords = "Newton step, Jacobian structure, Jacobian sparsity.",
       referred = "[Griewank2002VJS], [Hossain2002RtN].",
       year = "1996",
       ad_theotech = "Sparsity"
}


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