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- Title
Extending the Applicability of Cordero Type Iterative Method.
- Authors
Remesh, Krishnendu; Argyros, Ioannis K.; Saeed K, Muhammed; George, Santhosh; Padikkal, Jidesh
- Abstract
Symmetries play a vital role in the study of physical systems. For example, microworld and quantum physics problems are modeled on the principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Most of these studies reduce to solving nonlinear equations in suitable abstract spaces iteratively. In particular, the convergence of a sixth-order Cordero type iterative method for solving nonlinear equations was studied using Taylor expansion and assumptions on the derivatives of order up to six. In this study, we obtained order of convergence six for Cordero type method using assumptions only on the first derivative. Moreover, we modified Cordero's method and obtained an eighth-order iterative scheme. Further, we considered analogous iterative methods to solve an ill-posed problem in a Hilbert space setting.
- Subjects
TAYLOR'S series; NONLINEAR equations; HILBERT space; QUANTUM theory; PROBLEM solving; ITERATIVE methods (Mathematics)
- Publication
Symmetry (20738994), 2022, Vol 14, Issue 12, p2495
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym14122495