Modified Newton’s method for systems of nonlinear equations with singular Jacobian
✍ Scribed by José L. Hueso; Eulalia Martínez; Juan R. Torregrosa
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 417 KB
- Volume
- 224
- Category
- Article
- ISSN
- 0377-0427
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📜 SIMILAR VOLUMES
In this paper we study the convergence properties of Newton's sequence for analytic systems of equations with constant rank derivatives. Our main result is an alpha-theorem which ensures the convergence of Newton's sequence to a leastsquare solution of this system.
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 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