A faster King–Werner-type iteration and its convergence analysis. Issue 14 (25th October 2020)

• Record Type: Journal Article
• Authors: Sharma, Janak Raj; Argyros, Ioannis K.; Kumar, Sunil
• Is Part Of: Applicable analysis. Volume 99:Issue 14(2020)
• Page Start: 2526
• Page End: 2542
• Publication Date: 2020-10-25
• Subjects: King–Werner method -- local convergence -- semi-local convergence -- Banach space -- Euclidean space; 65H10 -- 65J10 -- 41A25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1569228
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We introduce a new faster two-step King–Werner-type iterative method for solving nonlinear equations. The methodology is based on rational Hermite interpolation. The local as well as semi-local convergence analyses are presented under weak center Lipschitz and Lipschitz conditions. The convergence order is increased from 1 + 2 to 3 without any additional function calculations. Another advantage is the convenient fact that this method does not use derivatives. Numerical examples further validate the theoretical results.