On the Reversibility of Newton-Raphson Root-Finding Method

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Reversibility of a computational method is the ability to execute the method forward as well as backward. Reversible computational methods are generally useful in undoing incorrect computation in a speculative execution setting designed for efficient parallel processing. Here, reversibility is explored of a common component in scientific codes, namely, the Newton-Raphson root-finding method. A reverse method is proposed that is aimed at retracing the sequence of points that are visited by the forward method during forward iterations. When given the root, along with the number of iterations, of the forward method, this reverse method is aimed at backtracking along the ... continued below

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Perumalla, Kalyan S.; Wright, John P. & Kuruganti, Phani Teja July 1, 2008.

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Reversibility of a computational method is the ability to execute the method forward as well as backward. Reversible computational methods are generally useful in undoing incorrect computation in a speculative execution setting designed for efficient parallel processing. Here, reversibility is explored of a common component in scientific codes, namely, the Newton-Raphson root-finding method. A reverse method is proposed that is aimed at retracing the sequence of points that are visited by the forward method during forward iterations. When given the root, along with the number of iterations, of the forward method, this reverse method is aimed at backtracking along the reverse sequence of points to finally recover the original starting point of the forward method. The operation of this reverse method is illustrated on a few example functions, serving to highlight the method's strengths and shortcomings.

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  • Report No.: ORNL/TM-2007/152
  • Grant Number: DE-AC05-00OR22725
  • DOI: 10.2172/934800 | External Link
  • Office of Scientific & Technical Information Report Number: 934800
  • Archival Resource Key: ark:/67531/metadc895068

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  • July 1, 2008

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

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  • Oct. 28, 2016, 2:44 p.m.

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Perumalla, Kalyan S.; Wright, John P. & Kuruganti, Phani Teja. On the Reversibility of Newton-Raphson Root-Finding Method, report, July 1, 2008; [Tennessee]. (digital.library.unt.edu/ark:/67531/metadc895068/: accessed May 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.