Abstract
A new semilocal convergence theorem for a fast iterative method in Banach spaces is provided for approximating a solution of a nondifferentiable operator equation. A condition for divided differences of order one is considered in this paper, which generalizes the usual ones, i.e., Lipschitz continuous or Hölder continuous conditions. Note that no conditions of divided differences of order two are used. Therefore our results are of theoretical and practical interest. Finally, a numerical example is provided to show that the new iterative method compares favorably with earlier ones.
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Ren, H., Argyros, I.K. A new semilocal convergence theorem for a fast iterative method with nondifferentiable operators. J. Appl. Math. Comput. 34, 39–46 (2010). https://doi.org/10.1007/s12190-009-0303-0
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DOI: https://doi.org/10.1007/s12190-009-0303-0
Keywords
- Semilocal convergence
- Iterative method
- Nondifferentiable operators
- Banach space
- Divided difference
- Quadratic convergence