The Newtonian Operator and Global Convergence Balls for Newton’s Method

José A. Ezquerro and Miguel A. Hernández-Verón
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José A. Ezquerro: Department of Mathematics and Computation, University of La Rioja, alle Madre de Dios, 53, 26006 Logroño, La Rioja, Spain
Miguel A. Hernández-Verón: Department of Mathematics and Computation, University of La Rioja, alle Madre de Dios, 53, 26006 Logroño, La Rioja, Spain

Mathematics, 2020, vol. 8, issue 7, 1-9

Abstract: We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.

Keywords: fixed-point theorem; Newton’s method; Newtonian operator; global convergence; convergence ball; Fredholm integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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