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On the Davidenko-Branin Method for Solving Simultaneous Nonlinear Equations

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1 Author(s)
R. P. Brent ; IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA

It has been conjectured that the Davidenko–Branin method for solving simultaneous nonlinear equations is globally convergent, provided that the surfaces on which each equation vanishes are homeomorphic to hyperplanes. We give an example to show that this conjecture is false. A more complicated example shows that the method may fail to converge to a zero of the gradient of a scalar function, so the associated method for function minimization is not globally convergent.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:16 ,  Issue: 4 )