Unified Local Convergence for Newton’s Method and Uniqueness of the Solution of Equations under Generalized Conditions in a Banach Space

Ioannis K. Argyros, Ángel Alberto Magreñán, Lara Orcos and Íñigo Sarría
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Ioannis K. Argyros: Department of Mathematics Sciences Lawton, Cameron University, Lawton, OK 73505, USA
Ángel Alberto Magreñán: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain
Lara Orcos: Facultad de Educación, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Íñigo Sarría: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain

Mathematics, 2019, vol. 7, issue 5, 1-13

Abstract: Under the hypotheses that a function and its Fréchet derivative satisfy some generalized Newton–Mysovskii conditions, precise estimates on the radii of the convergence balls of Newton’s method, and of the uniqueness ball for the solution of the equations, are given for Banach space-valued operators. Some of the existing results are improved with the advantages of larger convergence region, tighter error estimates on the distances involved, and at-least-as-precise information on the location of the solution. These advantages are obtained using the same functions and Lipschitz constants as in earlier studies. Numerical examples are used to test the theoretical results.

Keywords: Newton’s method; local convergence; Newton-Mysovskii conditions; Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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