A uniparametric family of iterative processes for solving nondifferentiable equations

By M. A. Hernández, M. J. Rubio. 2002

68 citations recorded by the source corpus.

In this work we study a class of secant-like iterations for solving nonlinear equations in Banach spaces. We consider a condition for divided differences which generalizes the usual ones, i.e., Lipschitz and Holder continuous conditions. A semilocal convergence result is obtained for nondifferentiable operators. For that, we use a technique based on a new system of recurrence relations to obtain domains of existence and uniqueness of the solution. Finally, we apply our results to the numerical solution of several examples.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b419ac8c32e68266de7ce42aeeffbb6117c3a34a

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In Computational Theory and Mathematics

1. Sonia Busquier
2. Sergio Amat

In Numerical Analysis

1. Sonia Busquier
2. Sergio Amat
3. Herbert H. H. Homeier
4. Sergio Plaza

Citations in the corpus

• A two-step Steffensen's method under modified convergence conditions (2006, methodology): “In this study, we present a semilocal convergence theorem under modified Kantorovich conditions [1,2,8,9] without assuming any Fréchet differentiability.”