A reliable argument principle algorithm to find the number of zeros of an analytic function in a bounded domain

Summary The argument principle is a natural and simple method to determine the number of zeros of an analytic functionf(z) in a bounded domainD. N, the number of zeros (counting multiplicities) off(z), is 1/2 times the change in Argf(z) asz moves along the closed contour D. Since the range of Argf(z) is (–, ] a critical point in the computational procedure is to assure that the discretization of D, {z_i,i=1, ...,M}, is such that. Discretization control which may violate this inequality can lead to an unreliable algorithm. Mathematical theorems derived for the discretization of D lead to a completely reliable algorithm to computeN. This algorithm also treats in an elementary way the case when a zero is on or near the contour D. Numerical examples are given for the reliable algorithm formulated here and it is pointed out in these examples how inadequate discretization control can lead to failure of other algorithms.Dedicated to Professor Ivo Babuka in commemoration of his sixtieth birthdayThis research is part of the doctoral dissertation of this author