Geodesic
Extended Convergence of a Two-Step-Secant-Type Method Under a Restricted Convergence Domain
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 1, p. 155

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We present a local as well as a semi-local convergence analysis of a two-step secant-type method for solving nonlinear equations involving Banach space valued operators. By using weakened Lipschitz and center Lipschitz conditions in combination with a more precise domain containing the iterates, we obtain tighter Lipschitz constants than in earlier studies. This technique lead to an extended convergence domain, more precise information on the location of the solution and tighter error bounds on the distances involved. These advantages are obtained under the same computational effort, since the new constants are special cases of the old ones used in earlier studies. The new technique can be used on other iterative methods. The numerical examples further illustrate the theoretical results.
Classification : 65D10, 65G99, 65D99, 47J05, 49M15
Keywords: two step secant-type method, local convergence, Banach space, restricted convergence domain, divided difference 
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Ioannis K. Argyros; Santhosh George. Extended Convergence of a Two-Step-Secant-Type Method Under a Restricted Convergence Domain. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 1, p. 155 . http://geodesic.mathdoc.fr/item/KJM_2021_45_1_a11/