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month = {May},
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year = {2016}
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}
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@INCOLLECTION{
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Kearfott1996ADo,
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author = "R. Baker Kearfott",
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editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
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title = "Automatic Differentiation of Conditional Branches in an Operator Overloading Context",
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booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
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pages = "75--81",
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publisher = "SIAM",
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address = "Philadelphia, PA",
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key = "Kearfott1996ADo",
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crossref = "Berz1996CDT",
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abstract = "In the past, it has been problematical to include {\tt IF-THEN-ELSE} branches
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in automatic differentiation processes driven by operator overloading and code list generation, when
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the branch condition contains variables. However, this problem can be circumvented with a special
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``branch function'' $\chi$. Definition of this function, formulas for its use, and
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implications of its use will be discussed. A second issue is: what can be done when derivatives are
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discontinuous? In fact, simple and meaningful Newton iterations can be set up when even the function
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itself is discontinuous. Simplified figures and examples are given, as well as references to
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in-depth explanations. An example of the convergence behavior is given with an interval Newton
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method to find critical points for the problem ``$\min |x|$.''",
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keywords = "Conditional branches, operator overloading, branch function, discontinuous
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derivatives.",
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referred = "[Berz2002TaU], [Dignath2002AAa].",
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year = "1996"
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}
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@INCOLLECTION{
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Tadjouddine2005ItP,
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author = "Mohamed Tadjouddine and Frances Bodman and John D. Pryce and Shaun A. Forth",
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title = "Improving the Performance of the Vertex Elimination Algorithm for Derivative
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Calculation",
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editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
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Norris",
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booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
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series = "Lecture Notes in Computational Science and Engineering",
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publisher = "Springer",
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year = "2005",
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abstract = "In previous work [TOMS, 2004, 30(3), 266--299], we used Markowitz-like heuristics
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to find elimination sequences that minimise the number of floating-point operations (flops) for
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vertex elimination Jacobian code. We also used the depth-first traversal algorithm to reorder the
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statements of the Jacobian code with the aim of reducing the number of memory accesses. In this
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work, we study the effects of reducing flops or memory accesses within the vertex elimination
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algorithm for Jacobian calculation. On RISC processors, we observed that for data residing in
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registers, the number of flops gives a good estimate of the execution time, while for
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out-of-register data, the execution time is dominated by the time for memory access operations. We
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also present a statement reordering scheme based on a greedy list scheduling algorithm using ranking
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functions. This statement reordering will enable us to trade off the exploitation of the instruction
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level parallelism of such processors with the reduction in memory accesses.",
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crossref = "Bucker2005ADA",
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ad_tools = "EliAD",
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ad_theotech = "X-Country",
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pages = "111--120",
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doi = "10.1007/3-540-28438-9_10"
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}
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@ARTICLE{
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Tadjouddine2008VoA,
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author = "Tadjouddine, E. M.",
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title = "{Vertex-ordering Algorithms for Automatic Differentiation of Computer Codes}",
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journal = "The Computer Journal",
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volume = "51",
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number = "6",
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pages = "688--699",
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doi = "10.1093/comjnl/bxm115",
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year = "2008",
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abstract = "In the context of Automatic Differentiation (AD) of functions represented by
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computer code via the vertex elimination approach first advocated by Griewank and Reese (On the
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Calculation of Jacobian Matrices by the Markowitz Rule. In Griewank, A. and Corliss, G.F. (eds),
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Automatic Differentiation of Algorithms: Theory, Implementation and Application, pp. 126-135. SIAM,
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1991, Philadelphia, PA.), we present two approximate algorithms based on the linearized
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computational graph of the input code. The first is a statement-reordering algorithm aiming to tune
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the AD-generated code so as to maximize its performance for modern superscalar processors. The
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second is aimed at detecting interface contractions introduced by Bischof and Haghighat
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(Hierarchical Approaches to Automatic Differentiation. In Berz, M., Bischof, C., Corliss, G. and
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Griewank, A. (eds), Computational Differentiation: Techniques, Applications, and Tools, pp. 83-94.
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SIAM, 1996, Philadelphia, PA) in order to enable exploitation of the structure of the input code in
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the differentiation process. Performance data are also presented.",
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url = "http://comjnl.oxfordjournals.org/cgi/content/abstract/51/6/688",
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eprint = "http://comjnl.oxfordjournals.org/cgi/reprint/51/6/688.pdf",
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ad_theotech = "Hierarchical Approach"
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}
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@INCOLLECTION{
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Griewank1991OtC,
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author = "Andreas Griewank and Shawn Reese",
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editor = "Andreas Griewank and George F. Corliss",
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title = "On the Calculation of {J}acobian Matrices by the {M}arkowitz Rule",
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booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application",
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pages = "126--135",
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publisher = "SIAM",
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address = "Philadelphia, PA",
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key = "Griewank1991OtC",
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crossref = "Griewank1991ADo",
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comment = "Also appeared as Preprint MCS--P267--1091, Mathematics and Computer Science
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Division, Argonne National Laboratory, Argonne, Ill., January 1992.",
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referred = "[Bischof1996HAt], [Corl91a]; [Feehery1996ADB], [Irim91a], [Naumann2002ETf],
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[Tadjouddine2001ATa].",
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isbn = "0--89871--284--X",
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year = "1991",
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ad_theotech = "X-Country"
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}
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