A family of optimal quadratic-order multiple-zero finders with a weight function of the principal kth root of a derivative-to-derivative ratio and their basins of attraction
Young, Hee Geum
Kim, Young Ik
MetadataShow full item record
Multiple-zero finders with optimal quartic convergence for nonlinear equations are proposed in this paper with a weight function of the principal kth root of a derivative-to-derivative ratio. The optimality of the proposed multiple-zero finders is checked for their consistency based on Kung–Traub’s conjecture established in 1974. Through various test equations, relevant numerical experiments strongly support the claimed theory in this paper. Also investigated are extraneous fixed points of the iterative maps associated with the proposed methods. Their dynamics is explored along with illustrated basins of attraction for various polynomials.
The article of record as published may be found at http://dx.doi.org/10.1016/j.matcom.2016.10.008
Showing items related by title, author, creator and subject.
Demetriou, M.A.; Fahroo, F. (IEEE, 2008);We consider a class of second order infinite dimensional bilinear systems with partial state observation. The objective is to design an observer for such a class of infinite dimensional systems that preserves the physical ...
Haegel, N.M.; Mills, T.J.; Talmadge, M.; Scandrett, C.L.; Frenzen, C.L.; Yoon, H.; Fetzer, C.M.; King, R.R. (IEEE., 2009);We consider a class of second order infinite dimensional bilinear systems with partial state observation. The objective is to design an observer for such a class of infinite dimensional systems that preserves the physical ...
A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics Neta, Beny; Geum, Young Hee; Kim, Young Ik (Elsevier Inc., 2015);Under the assumption of the known multiplicity of zeros of nonlinear equations, a class of two-point sextic-order multiple-zero finders and their dynamics are investigated in this paper by means of extensive analysis of ...