On the Davidenko-Branin method for solving simultaneous
nonlinear equations
8. R. P. Brent,
On the Davidenko-Branin method for solving simultaneous nonlinear equations,
IBM J. Research and Development 16 (1972), 434-436.
CR 14\#24419,
MR 48#12817.
Paper:
pdf (449K).
Abstract
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.
Errata
In the statement of Theorem 2 and the following remarks, there should
be a multiplier alpha inside the exponential. The theorem holds
for suitable alpha >1.
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