Miodrag S. Petković

Iterative methods for simultaneous inclusion of polynomial zeros

Basic concepts.- Iterative methods without derivatives.- Generalized root iterations.- Bells polynomials and parallel disk iterations.- Computational efficiency of simultaneous methods.

A family of three-point methods of optimal order for solving nonlinear equations

A family of three-point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters. It is proved that these methods have the convergence order eight requiring only four function evaluations per iteration. In this way it is demonstrated that the proposed class of methods supports the Kung-Traub hypothesis (1974) [3] on the upper bound 2^n of the order of multipoint methods based on n+1 function evaluations. Consequently, this class of root solvers possesses very high computational efficiency. Numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations.

On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency

A general class of

On the convergence order of a modified method for simultaneous finding polynomial zeros

n

Three-point methods with and without memory for solving nonlinear equations

-point iterative methods for solving nonlinear equations is constructed by combining methods of Newtons type and an arbitrary two-point method of the fourth order of convergence. It is proved that these methods have the convergence order

Multipoint methods for solving nonlinear equations: A survey

2^n

An improvement of Gargantini's simultaneous inclusion method for polynomial roots by Schro¨der's correction

, requiring only

Remarks on “On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency”

n+1

On a generalisation of the root iterations for polynomial complex zeros in circular interval arithmetic

function evaluations per iteration. In this way it is demonstrated that the proposed class of methods supports the Kung-Traub hypothesis (1974) on the upper bound

Point estimation of root finding methods

2^n