Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems
- Hernández-Verón, M.A. 1
- Martínez, E. 2
- Teruel, C. 2
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1
Universidad de La Rioja
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2
Universidad Politécnica de Valencia
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ISSN: 1017-1398
Argitalpen urtea: 2017
Alea: 76
Zenbakia: 2
Orrialdeak: 309-331
Mota: Artikulua
Beste argitalpen batzuk: Numerical Algorithms
Lotura duten proiektuak
Laburpena
In this paper, we analyze the semilocal convergence of k-steps Newton’s method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the Fréchet derivative satisfies the Lipschitz continuity, we define appropriate recurrence relations for obtaining the domains of convergence and uniqueness. We also define the accessibility regions for this iterative process in order to guarantee the semilocal convergence and perform a complete study of their efficiency. Our final aim is to apply these theoretical results to solve a special kind of conservative systems. © 2016 Springer Science+Business Media New York