Impact on Stability by the Use of Memory in Traub-Type Schemes

Francisco I. Chicharro, Alicia Cordero, Neus Garrido and Juan R. Torregrosa
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Francisco I. Chicharro: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Neus Garrido: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain

Mathematics, 2020, vol. 8, issue 2, 1-16

Abstract: In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub’s method, they have been designed using linear approximations or the Newton’s interpolation polynomials. In both cases, the parameters use information from the current and the previous iterations, so they define a method with memory. Moreover, they achieve higher order of convergence than Traub’s scheme without any additional functional evaluations. The real dynamical analysis verifies that the proposed methods with memory not only converge faster, but they are also more stable than the original scheme. The methods selected by means of this analysis can be applied for solving nonlinear problems with a wider set of initial estimations than their original partners. This fact also involves a lower number of iterations in the process.

Keywords: nonlinear dynamics; iterative methods with memory; multidimensional dynamics; accelerator parameter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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