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Author(s) Petkovic, M., Vranic, D.
Title On the guaranteed convergence of a family of simultaneous iterative methods
Abstract The construction of initial conditions which guarantee the safe convergence of iterative processes is one of the most important problems in solving nonlinear equations. In this paper we give initial conditions for a one parameter family of square-root iteration methods for the simultaneous approximation of all simple zeros of a polynomial. This family, based on the Hansen-Patrick third order method, has also the cubic convergence and generates some new methods. The presented initial conditions are of practical importance since depend only of available data: coefficients of a polynomial and initial approximations to the wanted zeros of a polynomial.
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