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Newton’s Like Normal S-iteration under Weak Conditions
Version 1
: Received: 19 October 2022 / Approved: 31 October 2022 / Online: 31 October 2022 (02:23:04 CET)
A peer-reviewed article of this Preprint also exists.
Singh, M.K.; Argyros, I.K.; Singh, A.K. Newton-like Normal S-iteration under Weak Conditions. Axioms 2023, 12, 283. Singh, M.K.; Argyros, I.K.; Singh, A.K. Newton-like Normal S-iteration under Weak Conditions. Axioms 2023, 12, 283.
Abstract
In the present paper, we introduced a quadratically convergent Newton’s like normal S2 iteration method free from the second derivative for the solution of nonlinear equations permitting 3 f'(x) = 0 at some points in the neighborhood of the root. Our proposed method works well 4 when the Newton method fails. Numerically it has been verified that the Newton’s like normal 5 S-iteration method converges faster than Fang et al. method [A cubically convergent Newton-type 6 method under weak conditions, J. Compute. and Appl. Math., 220 (2008), 409-412]. We studied 7 different aspects of normal S-iteration method. Lastly, fractal patterns support the numerical 8 results and explain the convergence, divergence, and stability of method.
Keywords
Newton’s method; normal S-iteration; weak condition; simple root
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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