www.Autodiff.org - Publication: Reducing the Number of AD Passes for Computing a Sparse Jacobian Matrix

Reducing the Number of AD Passes for Computing a Sparse Jacobian Matrix

- incollection -

Author(s)
Shahadat Hossain , Trond Steihaug

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
A reduction in the computational work is possible if we do not require that the nonzeros of a Jacobian matrix be determined directly. If a column or row partition is available, the proposed substitution technique can be used to reduce the number of groups in the partition further. In this chapter, we present a substitution method to determine the structure of sparse Jacobian matrices efficiently using forward, reverse, or a combination of forward and reverse modes of ad. Specifically, if it is true that the difference between the maximum number of nonzeros in a column or row and the number of groups in the corresponding partition is large, then the proposed method can save many ad passes. This assertion is supported by numerical examples.

Cross-References
Corliss2002ADo

AD Theory and Techniques
Sparsity

BibTeX
@INCOLLECTION{
         Hossain2002RtN,
       author = "Shahadat Hossain and Trond Steihaug",
       title = "Reducing the Number of {AD} Passes for Computing a Sparse {J}acobian Matrix",
       pages = "263--270",
       abstract = "A reduction in the computational work is possible if we do not require that the
         nonzeros of a Jacobian matrix be determined directly. If a column or row partition is available, the
         proposed substitution technique can be used to reduce the number of groups in the partition further.
         In this chapter, we present a substitution method to determine the structure of sparse Jacobian
         matrices efficiently using forward, reverse, or a combination of forward and reverse modes of AD.
         Specifically, if it is true that the difference between the maximum number of nonzeros in a column
         or row and the number of groups in the corresponding partition is large, then the proposed method
         can save many AD passes. This assertion is supported by numerical examples.",
       chapter = "31",
       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",
       referred = "[Klein2002DMf].",
       ad_theotech = "Sparsity"
}

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