论文信息 - Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods

Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods

In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King's family of fourth-order schemes is obtained as an special case. We also present results for describing the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees.

Alicia Cordero | Juan R. Torregrosa | Santiago Artidiello | Francisco Chicharro

[1] S. Amat,et al. Review of some iterative root-finding methods from a dynamical point of view , 2004 .

[2] V. Drakopoulos. HOW IS THE DYNAMICS OF KÖNIG ITERATION FUNCTIONS AFFECTED BY THEIR ADDITIONAL FIXED POINTS , 1999 .

[3] Changbum Chun,et al. On optimal fourth-order iterative methods free from second derivative and their dynamics , 2012, Appl. Math. Comput..

[4] John H. Hubbard,et al. On the dynamics of polynomial-like mappings , 1985 .

[5] Kyle Kneisl,et al. Julia sets for the super-Newton method, Cauchy's method, and Halley's method. , 2001, Chaos.

[6] J. Traub. Iterative Methods for the Solution of Equations , 1982 .

[7] Xia Wang,et al. Two new families of sixth-order methods for solving non-linear equations , 2009, Appl. Math. Comput..

[8] H. Hussein,et al. The Dynamics of Newton's Method on Complex Quartic Polynomial , 2012 .

[9] H. T. Kung,et al. Optimal Order of One-Point and Multipoint Iteration , 1974, JACM.

[10] M. Matinfar,et al. Three-step iterative methods with eighth-order convergence for solving nonlinear equations , 2013 .

[11] R. F. King. A Family of Fourth Order Methods for Nonlinear Equations , 1973 .