New Improvement of the Domain of Parameters for Newton’s Method

Cristina Amorós, Ioannis K. Argyros, Daniel González, Ángel Alberto Magreñán, Samundra Regmi and Íñigo Sarría
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Cristina Amorós: Escuela Superior de Ingeniería y Tecnología, UNIR, 26006 Logroño, Spain
Ioannis K. Argyros: Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Daniel González: Escuela de Ciencias Físicas y Matemáticas, Universidad de las Americas, Quito 170517, Ecuador
Ángel Alberto Magreñán: Departamento de Matemáticas y Computación, Universidad de la Rioja, 26004 Logroño, Spain
Samundra Regmi: Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Íñigo Sarría: Escuela Superior de Ingeniería y Tecnología, UNIR, 26006 Logroño, Spain

Mathematics, 2020, vol. 8, issue 1, 1-12

Abstract: There is a need to extend the convergence domain of iterative methods for computing a locally unique solution of Banach space valued operator equations. This is because the domain is small in general, limiting the applicability of the methods. The new idea involves the construction of a tighter set than the ones used before also containing the iterates leading to at least as tight Lipschitz parameters and consequently a finer local as well as a semi-local convergence analysis. We used Newton’s method to demonstrate our technique. However, our technique can be used to extend the applicability of other methods too in an analogous manner. In particular, the new information related to the location of the solution improves the one in previous studies. This work also includes numerical examples that validate the proven results.

Keywords: domain; Newton’s method; improvement (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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