1806	 On the Downhill Method	 The downhill method is a numerical method for solving complex equations f z 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 . Some numerical examples are included. downhill method complex relaxation method complex iteration complex equation transcendental complex equation algebraic complex equation
