A COMPUTER PROGRAM FOR FINDING COMPLEX ZEROS OF AN ARBITRARY FUNCTION

摘要

The first part of this report describes a computer programme which finds com¬plex zeros of arbitrary functions by iteration from some given initial guesses. The basis of the iteration is to approximate the given function by simpler func¬tions whose zeros can be simply calculated. The regions of the complex plane in which the iteration converges to a required zero are greatly extended by several ad hoc procedures developed in a study of helicon wave propagation. The programme is constructed in such a way as to allow indefinite extension of the facilities offered without reference to the original programming. The helicon wave problem is used as an illustrative example and simple methods by which more complicated eigenvalue problems can be solved are indicated.