Purely Iterative Algorithms for Newton’s Maps and General Convergence

Sergio Amat, Rodrigo Castro, Gerardo Honorato and Á. A. Magreñán
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Sergio Amat: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
Rodrigo Castro: Facultad de Ciencias, Universidad de Valparaíso, Valparaíso 2340000, Chile
Gerardo Honorato: CIMFAV and Institute of Mathematical Engineering, Universidad de Valparaíso, General Cruz 222, Valparaíso 2340000, Chile
Á. A. Magreñán: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006 Logroño, Spain

Mathematics, 2020, vol. 8, issue 7, 1-27

Abstract: The aim of this paper is to study the local dynamical behaviour of a broad class of purely iterative algorithms for Newton’s maps. In particular, we describe the nature and stability of fixed points and provide a type of scaling theorem. Based on those results, we apply a rigidity theorem in order to study the parameter space of cubic polynomials, for a large class of new root finding algorithms. Finally, we study the relations between critical points and the parameter space.

Keywords: general convergence; cubic polynomials; purely iterative methods; Lipschitz conditions; dynamics (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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