Anomalies in the convergence of Traub‐type methods with memory. Issue 1 (3rd September 2019)

• Record Type: Journal Article
• Authors: Chicharro, Francisco I.; Cordero, Alicia; Garrido, Neus; Torregrosa, Juan R.
• Is Part Of: Computational and mathematical methods. Volume 2:Issue 1(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-09-03
• Subjects: basin of attraction -- fixed points -- iterative process with memory -- nonlinear equation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1060
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : The stability analysis of a new family of iterative methods with memory is introduced. This family, designed from Traub's method, allows to add memory through the introduction of an accelerating parameter. Hence, the speed of convergence of the iterative method increases up to 3.30, with no new functional evaluations. A dynamical study of the proposed family on quadratic polynomials is presented obtaining interesting qualitative properties.