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- Title
Local convergence of a parameter based iteration with Hölder continuous derivative in Banach spaces.
- Authors
Singh, Sukhjit; Gupta, D.; Badoni, Rakesh; Martínez, E.; Hueso, José
- Abstract
The local convergence analysis of a parameter based iteration with Hölder continuous first derivative is studied for finding solutions of nonlinear equations in Banach spaces. It generalizes the local convergence analysis under Lipschitz continuous first derivative. The main contribution is to show the applicability to those problems for which Lipschitz condition fails without using higher order derivatives. An existence-uniqueness theorem along with the derivation of error bounds for the solution is established. Different numerical examples including nonlinear Hammerstein equation are solved. The radii of balls of convergence for them are obtained. Substantial improvements of these radii are found in comparison to some other existing methods under similar conditions for all examples considered.
- Subjects
STOCHASTIC convergence; PARAMETERS (Statistics); ITERATIVE methods (Mathematics); DERIVATIVES (Mathematics); BANACH spaces; NONLINEAR equations
- Publication
Calcolo, 2017, Vol 54, Issue 2, p527
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-016-0197-9