A class of four parametric with‐ and without‐memory root finding methods. Issue 3 (22nd April 2019)

• Record Type: Journal Article
• Authors: Zafar, Fiza; Cordero, Alicia; Torregrosa, Juan R.; Rafi, Aneeqa
• Is Part Of: Computational and mathematical methods. Volume 1:Issue 3(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-04-22
• Subjects: iterative methods -- Kung‐Traub conjecture -- with‐memory method; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1024
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : In this paper, we have constructed a derivative‐free weighted eighth‐order iterative method with and without memory for solving nonlinear equations. This method is an optimal method as it satisfies the Kung‐Traub conjecture. We have used four accelerating parameters, a univariate and a multivariate weight function at the second and third step of the method, respectively. This method is converted into with‐memory method by approximating the parameters using Newton's interpolating polynomials of appropriate degree to increase the order of convergence to 15.51560 and the efficiency index is nearly two. Numerical comparison of our methods is done with the recent methods of respective domain.