A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton-Kantorovich Iterations

Samundra Regmi, Ioannis K. Argyros, Santhosh George and Christopher I. Argyros
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Samundra Regmi: Learning Commons, University of North Texas at Dallas, Dallas, TX 75201, USA
Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Santhosh George: Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India
Christopher I. Argyros: Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA

Mathematics, 2022, vol. 10, issue 8, 1-14

Abstract: There are a plethora of semi-local convergence results for Newton’s method (NM). These results rely on the Newton–Kantorovich criterion. However, this condition may not be satisfied even in the case of scalar equations. For this reason, we first present a comparative study of established classical and modern results. Moreover, using recurrent functions and at least as small constants or majorant functions, a finer convergence analysis for NM can be provided. The new constants and functions are specializations of earlier ones; hence, no new conditions are required to show convergence of NM. The technique is useful on other iterative methods as well. Numerical examples complement the theoretical results.

Keywords: iterative methods; Banach space; semi-local convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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