On the Reversibility of Newton-Raphson Root-Finding Method

Perumalla, Kalyan S. ; Wright, John P. ; Kuruganti, Phani Teja

Oak Ridge National Laboratory

关键词: Research Programs;    Mathematics;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Parallel Processing;    97;   

DOI  :  10.2172/934800
RP-ID  :  ORNL/TM-2007/152
RP-ID  :  DE-AC05-00OR22725
RP-ID  :  934800

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.