A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

We introduce a new class of optimal iterative methods without memory for approximating a simple root of a given nonlinear equation. The proposed class uses four function evaluations and one first derivative evaluation per iteration and it is therefore optimal in the sense of Kung and Traub's conjecture. We present the construction, convergence analysis and numerical implementations, as well as comparisons of accuracy and basins of attraction between our method and existing optimal methods for several test problems.

Details

Original languageEnglish
Pages (from-to)69-90
Number of pages22
JournalMathematics and Computers in Simulation
Volume119
Publication statusPublished - 1 Jan 2016
Peer-reviewedYes

External IDs

ORCID /0000-0003-0967-6747/work/213148716

Keywords

Keywords

  • Computational efficiency, Four-step iterative method, Kung and Traub conjecture, Optimal order of convergence, Simple root