Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications

Volume 11, Issue 11, pp 1215--1224 http://dx.doi.org/10.22436/jnsa.011.11.01 Publication Date: August 01, 2018       Article History

Authors

Ioannis K. Argyros - Cameron University, Department of Mathematics Sciences Lawton, OK 73505, USA Alberto Magreñán - Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Universidad Internacional de La Rioja, Av de la Paz, 137, 26002 Logroño, Spain Íñigo Sarría - Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Universidad Internacional de La Rioja, Av de la Paz, 137, 26002 Logroño, Spain Juan Antonio Sicilia - Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Universidad Internacional de La Rioja, Av de la Paz, 137, 26002 Logroño, Spain


Abstract

In this paper, we are concerned with the problem of approximating a solution of a nonlinear equations by means of using the Secant method. We present a new semilocal convergence analysis for Secant method using restricted convergence domains. According to this idea we find a more precise domain where the inverses of the operators involved exist than in earlier studies. This way we obtain smaller Lipschitz constants leading to more precise majorizing sequences. Our convergence criteria are weaker and the error bounds are more precise than in earlier studies. Under the same computational cost on the parameters involved our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Different real-world applications are also presented to illustrate the theoretical results obtained in this study.


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