On the Downhill Method
The downhill method is a numerical method for
solving complex equations f(z) = 0 on which the 
only restriction is that the function w = f(z) must
be analytical.  An introduction to this method is 
given and a critical review of relating literature is
presented.  Although in theory the method always 
converges, it is shown that a fundamental dilemma exists
which may cause a breakdown in practical applications. 
 To avoid this difficulty and to improve the rate of
convergence toward a root, some modifications of 
the original method are proposed and a program (FORTRAN)
based on the modified method is given in Algorithm 
365.  Some numerical examples are included.
CACM December, 1969
Bach, H.
