A family of simultaneous methods for the determination of polynomial complex zeros

Abstract

Using the development of a rational function by elementary fractions, a family of methods for the simultaneous determination of polynomial complex zeros is derived. All the methods of the family are cubically convergent for simple zeros. The known simultaneous procedures of the third order are included. The presented class of iteration functions is suitable for the parallel inclusion of polynomial complex zeros by circular regions. The family of methods, defined in complex circular arithmetic, gives a new interval method with cubic convergence. Numerical example is given.