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Title: On the Reversibility of Newton-Raphson Root-Finding Method

On the Reversibility of Newton-Raphson Root-Finding Method 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.
Authors: ; ;
Publication Date:
OSTI Identifier:934800
Report Number(s):ORNL/TM-2007/152
TRN: US200815%%176
DOE Contract Number:DE-AC05-00OR22725
Resource Type:Technical Report
Data Type:
Research Org:Oak Ridge National Laboratory (ORNL); Center for Computational Sciences
Sponsoring Org:ORNL LDRD Director's R&D
Country of Publication:United States
Language:English
Subject: 97; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PARALLEL PROCESSING; MATHEMATICS; RESEARCH PROGRAMS