In this paper we consider constructing some higher-order modifications of Newton's method for solving nonlinear equations which increase the order of convergence of existing iterative methods by one or two or three units. This construction can be applied to any iteration formula, and per iteration t
Dynamics of Newton's method for solving some equations
β Scribed by Moonja Jeong; Gi Ok Kim; Seong-A Kim
- Book ID
- 114109404
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 465 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0097-8493
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π SIMILAR VOLUMES
The Lagrangian globalization (LG) method for non-linear equation-solving proposed in [ 101 is developed through theoretical analysis, the formulation of a particular LG algorithm, and a numerical illustration. New merit functions (termed detour potentials) for non-linear equation-solving, which broa
step iterative method Order of convergence a b s t r a c t In [YoonMee Ham etal., Some higher-order modifications of Newton's method for solving nonlinear equations, J. Comput. Appl. Math., 222 (2008) 477-486], some higher-order modifications of Newton's method for solving nonlinear equations are c
In this paper, modifications of a generalized Newton method based on some rules of quadrature are studied. The methods considered are Newton-like iterative schemes for numerical solving systems of nonsmooth equations. Some mild conditions are given that ensure superlinear convergence to a solution.