Convergence conditions for the secant method
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Ioannis K. Argyros
iargyros@cameron.edu
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Saïd Hilout
iargyros@cameron.edu
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DOI:
https://doi.org/10.4067/S0719-06462010000100014Abstract
We provide new sufficient convergence conditions for the convergence of the Secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, Lipschitz–type and center–Lipschitz–type instead of just Lipschitz–type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions are violated. Numerical examples are also provided in this study.
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Published
2010-03-01
How to Cite
[1]
I. K. Argyros and S. Hilout, “Convergence conditions for the secant method”, CUBO, vol. 12, no. 1, pp. 161–174, Mar. 2010.
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