An Improvement of Ostrowski’s and King’s Techniques with Optimal Convergence Order Eight
✍ Scribed by Fazlollah Soleymani; Mahdi Sharifi; Bibi Somayeh Mousavi
- Book ID
- 106433495
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 430 KB
- Volume
- 153
- Category
- Article
- ISSN
- 0022-3239
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In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. Each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices
## a b s t r a c t In this paper, we present two new iterative methods for solving nonlinear equations by using suitable Taylor and divided difference approximations. Both methods are obtained by modifying Potra-Pták's method trying to get optimal order. We prove that the new methods reach orders