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Kantorovich's type theorems for systems of equations with constant rank derivatives
- Source :
-
Journal of Computational & Applied Mathematics . Sep2008, Vol. 219 Issue 1, p110-122. 13p. - Publication Year :
- 2008
-
Abstract
- Abstract: The famous Newton–Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton''s method to a solution of an equation. Here we present a “Kantorovich type” convergence analysis for the Gauss–Newton''s method which improves the result in [W.M. Häußler, A Kantorovich-type convergence analysis for the Gauss–Newton-method, Numer. Math. 48 (1986) 119–125.] and extends the main theorem in [I.K. Argyros, On the Newton-Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. 169 (2004) 315–332]. Furthermore, the radius of convergence ball is also obtained. [Copyright &y& Elsevier]
- Subjects :
- *NEWTON-Raphson method
*STOCHASTIC convergence
*DIFFERENTIAL equations
*HYPOTHESIS
Subjects
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 219
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 32733963
- Full Text :
- https://doi.org/10.1016/j.cam.2007.07.006