Geodesic
Extending the convergence region of m-step iterative procedures
Serdica Mathematical Journal, Tome 47 (2022) no. 2, pp. 93-106.

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The convergence region of iterative procedures is small in general, and it becomes smaller as m increases. This problem limits the choice of starting points, and consequently the applicability of these methods. The novelty of this work lies in the fact that, we extend the convergence region by using specializations of the Lipschitz constants used before. Further advantages include improved error estimations and uniqueness results. The results are tested favorably to us on examples.
Keywords: m-step iterative methods, Banach space, semi-local convergence, Newton's method, Lipschitz continuity, 65F08, 37F50, 65N12 
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     title = {Extending the convergence region of m-step iterative procedures},
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Argyros, Ioannis; George, Santhosh. Extending the convergence region of m-step iterative procedures. Serdica Mathematical Journal, Tome 47 (2022) no. 2, pp. 93-106. http://geodesic.mathdoc.fr/item/SMJ2_2022_47_2_a0/