Borsch-Supan-like methods: Point estimation and parallel implementation

In this paper we consider Borsch-Supan's method and its modification with Weierstrass' correction. These methods are suitable for the simultaneous approximation of all simple zeros of polynominals and have the convergence order three and four, respectively. In the first part we give an initial condition for the safe convergence of the method with correction. This condition depends only on attainable data and has a practical importance. In the second part the comparison of the considered two methods on MIMD parallel computers (synchronous and asynchronous implementation) are studied.