MULTIPLICATIONAL COMBINATIONS AND A GENERAL SCHEME OF SINGLE-STEP ITERATIVE METHODS FOR MULTIPLE ROOTS
In this paper, a general form of single-step iterative methods for multiple roots of nonlinear equations is derived under a number of assumptions of optimization. Definition of multiplicational combinations and their properties are used upon the optimization procedure. Among all, we construct a family of iterative methods with nine parameters and simplest terms, and we obtain 23 simplest iterative methods within the family, those including all existing methods of single-step scheme. Numerical comparisons between the methods also present interesting and noteworthy results.
iterative methods multiple roots nonlinear equations newton's method single-step methods cubic order