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# A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions

Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de la Rioja, Av. La Paz 137, 26006 Logroño, Spain
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Mathematics 2020, 8(12), 2194; https://doi.org/10.3390/math8122194
Received: 14 November 2020 / Revised: 30 November 2020 / Accepted: 7 December 2020 / Published: 9 December 2020
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems 2020)
A straightforward family of one-point multiple-root iterative methods is introduced. The family is generated using the technique of weight functions. The order of convergence of the family is determined in its convergence analysis, which shows the constraints that the weight function must satisfy to achieve order three. In this sense, a family of iterative methods can be obtained with a suitable design of the weight function. That is, an iterative algorithm that depends on one or more parameters is designed. This family of iterative methods, starting with proper initial estimations, generates a sequence of approximations to the solution of a problem. A dynamical analysis is also included in the manuscript to study the long-term behavior of the family depending on the parameter value and the initial guess considered. This analysis reveals the good properties of the family for a wide range of values of the parameter. In addition, a numerical test on academic and engineering multiple-root functions is performed. View Full-Text
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MDPI and ACS Style

Chicharro, F.I.; Contreras, R.A.; Garrido, N. A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions. Mathematics 2020, 8, 2194. https://doi.org/10.3390/math8122194

AMA Style

Chicharro FI, Contreras RA, Garrido N. A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions. Mathematics. 2020; 8(12):2194. https://doi.org/10.3390/math8122194

Chicago/Turabian Style

Chicharro, Francisco I., Rafael A. Contreras, and Neus Garrido. 2020. "A Family of Multiple-Root Finding Iterative Methods Based on Weight Functions" Mathematics 8, no. 12: 2194. https://doi.org/10.3390/math8122194

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