Fast automatic differentiation Jacobians by compact LU factorization

Pryce, John D. ORCID: https://orcid.org/0000-0003-1702-7624 and Tadjouddine, Emmanuel M. 2008. Fast automatic differentiation Jacobians by compact LU factorization. SIAM Journal on Scientific Computing 30 (4) , pp. 1659-1677. 10.1137/050644847

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Abstract

For a vector function coded without branches or loops, a code for the Jacobian is generated by interpreting Griewank and Reese's vertex elimination as Gaussian elimination and implementing this as compact LU factorization. Tests on several platforms show such a code is typically 4 to 20 times faster than that produced by tools such as Adifor, Tamc, or Tapenade, on average significantly faster than vertex elimination code produced by the EliAD tool [Tadjouddine et al., in Proceedings of ICCS (2), Lecture Notes in Comput. Sci. 2330, Springer, New York, 2002] and can outperform a hand-coded Jacobian. The LU approach is promising, e.g., for CFD flux functions that are central to assembling Jacobians in finite element or finite volume calculations and, in general, for any inner-loop basic block whose Jacobian is crucial to an overall computation involving derivatives.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	automatic differentiation; vertex elimination; source transformation; abstract computational graph; sparse matrix; LU factorization
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/1064-8275/ (accessed 28/02/2014).
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	1064-8275
Date of First Compliant Deposit:	30 March 2016
Last Modified:	18 May 2023 09:00
URI:	https://orca.cardiff.ac.uk/id/eprint/49127

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