An automatic search procedure for finding real zeros

Summary The paper describes the implementation of a globally convergent iterative algorithm for determining all the real zeros of certain classes of functions in any given interval. The algorithm is developed in terms of Ostrowski's square root formula and in the case of polynomials the relation with Laguerre's formula is obtained. A device is incorporated for overcoming the problem of numerical instability together with a number of associated devices for ensuring that no zeros have been missed. Application of the method is illustrated by two examples having clustered zeros.