Please use this identifier to cite or link to this item:
|Title:||Convergence for variants of chebyshev-halley methods using restricted convergence domains|
|Citation:||Applicationes Mathematicae , Vol. 46 , 1 , p. 115 - 126|
|Abstract:||We present a local convergence analysis for some variants of Chebyshev-Halley methods of approximating a locally unique solution of a nonlinear equation in a Banach space setting. We only use hypotheses reaching up to the second Frechet derivative of the operator involved in contrast to earlier studies using Lipschitz hypotheses on the second Frechet derivative and other more restrictive conditions. This way the applicability of these methods is expanded. We also show how to improve the semilocal convergence in the earlier studies under the same conditions using our new idea of restricted convergence domains leading to: weaker sufficient conver- gence criteria, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. Numerical examples where earlier results cannot be applied but our results can, are also provided. © Instytut Matematyczny PAN, 2019.|
|Appears in Collections:||1. Journal Articles|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.