Enhancing Equation Solving: Extending the Applicability of Steffensen-Type Methods

Ramandeep Behl (), Ioannis K. Argyros and Monairah Alansari
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Ramandeep Behl: Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ioannis K. Argyros: Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Monairah Alansari: Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2023, vol. 11, issue 21, 1-19

Abstract: Local convergence analysis is mostly carried out using the Taylor series expansion approach, which requires the utilization of high-order derivatives, not iterative methods. There are other limitations to this approach, such as the following: the analysis is limited to finite-dimensional Euclidean spaces; no a priori computable error bounds on the distance or uniqueness of the solution results are provided. The local convergence analysis in this paper positively addresses these concerns in the more general setting of a Banach space. The convergence conditions involve only the operators in the methods. The more important semi-local convergence analysis not studied before is developed by using majorizing sequences. Both types of convergence analyses are based on the concept of generalized continuity. Although we study a certain class of methods, the same approach applies to extend the applicability of other schemes along the same lines.

Keywords: Steffensen’s method; convergence; divided difference; Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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