On the new fourth-order methods for the simultaneous approximation of polynomial zeros

Authors:
M. S. Petković;L. Rančić;M. R. Milošević
Affiliations:
Faculty of Electronic Engineering, Department of Mathematics, University of Niš, 18000 Niš, Serbia;Faculty of Electronic Engineering, Department of Mathematics, University of Niš, 18000 Niš, Serbia;Faculty of Science, Department of Mathematics and Informatics, University of Niš, 18000 Niš, Serbia
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 6
Cited 3

A bibliography on roots of polynomials

Journal of Computational and Applied Mathematics
The theory of Smale's point estimation and its applications

Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Some simultaneous iterations for finding all zeros of a polynomial with high order convergence

Applied Mathematics and Computation
Point estimation of simultaneous methods for solving polynomial equations: a survey

Journal of Computational and Applied Mathematics
Point estimation of simultaneous methods for solving polynomial equations: A survey (II)

Journal of Computational and Applied Mathematics
New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems

Journal of Complexity

Laguerre-like inclusion method for polynomial zeros

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Letter to the editor: A note on the improved derivative free root-solvers

Journal of Computational and Applied Mathematics
Iterative methods for solving nonlinear equations with finitely many roots in an interval

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

A new iterative method of the fourth-order for the simultaneous determination of polynomial zeros is proposed. This method is based on a suitable zero-relation derived from the fourth-order method for a single zero belonging to the Schroder basic sequence. One of the most important problems in solving polynomial equations, the construction of initial conditions that enable both guaranteed and fast convergence, is studied in detail for the proposed method. These conditions are computationally verifiable since they depend only on initial approximations, the polynomial coefficients and the polynomial degree, which is of practical importance. The construction of improved methods in ordinary complex arithmetic and complex circular arithmetic is discussed. Finally, numerical examples and the comparison with existing fourth-order methods are given.