On the Convergence of Secant-Like Methods

I. K. Argyros (), M. A. Hernández-Verón () and M. J. Rubio ()
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I. K. Argyros: Cameron University, Dept. of Mathematics Sciences
M. A. Hernández-Verón: University of La Rioja, Dept. of Mathematics and Computation
M. J. Rubio: University of La Rioja, Dept. of Mathematics and Computation

Chapter Chapter 5 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 141-183 from Springer

Abstract: Abstract In this chapter, our first idea is to improve the speed of convergence of the Secant method by means of iterative processes free of derivatives of the operator in their algorithms. To achieve this, we consider a uniparametric family of Secant-like methods previously constructed. We analyze the semilocal convergence of this uniparametric family of iterative processes by using a technique that consists of a new system of recurrence relations.

Keywords: Nonlinear equation; Non-differentiable operator; Divided difference; Iterative method; The Secant method; Local convergence; Semilocal convergence (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-15242-0_5

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DOI: 10.1007/978-3-030-15242-0_5

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