A family of multi-point iterative methods for solving systems of nonlinear equations
β Scribed by Gyurhan H. Nedzhibov
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 362 KB
- Volume
- 222
- Category
- Article
- ISSN
- 0377-0427
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β¦ Synopsis
We extend to n-dimensional case a known multi-point family of iterative methods for solving nonlinear equations. This family includes as particular cases some well known and also some new methods. The main advantage of these methods is they have order three or four and they do not require the evaluation of any second or higher order FrΓ©chet derivatives. A local convergence analysis and numerical examples are provided.
π SIMILAR VOLUMES
A family of three-point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters. It is proved that these methods have the convergence order eight requiring only four function evaluations per iteration. In this way it is
x,,, -J, m = 1, 2, 3 . . be an iteration method for solving the nonlinear problem F(X) = 0, where F(X) and its derivatives possess all of the properties required by T(x,,,). Then ifit can be established thatfor the problem at hand jlF(~,+ 1)i/ < &,, llF(x& V m > M,, (M, < co) and 0 < &,, < 1, dejini