An extension of a theorem by Wang for Smale's α-theory and applications

Autor: Magreñán Ruiz, Angel Alberto; Argyros, I.K.; 

Tipo de documento: Artículo de revista

Revista: Numerical Algorithms. ISSN: 1017-1398. Año: 2015. Número: 1. Volumen: 68. Páginas: 47-60.

Texto completo open access 

JCR (datos correspondientes al año 2014):
Edición:
Science  Área: MATHEMATICS, APPLIED  Quartil: Q1  Lugar área: 46/255  F. impacto: 1,417 

SCIMAGO (datos correspondientes al año 2014):
SJR:
1,168  SNIP: 1,416 

CIRC: GRUPO A

Referencias:

  • Amat, S., Busquier, S., Negra, M., Adaptive approximation of nonlinear operators (2004) Numer. Funct. Anal. Optim., 25, pp. 397-405
  • Argyros, I.K., Chui, C.K., Wuytack, L., Computational theory of iterative methods (2007) Series: Studies in Computational Mathematics, p. 15. , Elsevier, New York
  • Argyros, I.K.: A new semilocal convergence theorem for Newton’s method under a gamma-type condition. Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 56, 31–40 (2008/09)Argyros, I.K., A semilocal convergence analysis for directional Newton methods (2011) Math. Comput., 80, pp. 327-343
  • Argyros, I.K., Hilout, S., Weaker conditions for the convergence of Newton’s method (2012) J. Complex., 28, pp. 364-387
  • Argyros, I.K., Hilout, S., Convergence of Newton’s method under weak majorant condition (2012) J. Comput. Appl. Math., 236, pp. 1892-1902
  • Argyros, I.K., Cho, Y.J., Hilout, S., (2012) Numerical methods for equations and its applications, , CRC Press/Taylor and Francis Publ., New York
  • Cianciaruso, F., Convergence of Newton-Kantorovich approximations to an approximate zero (2007) Numer. Funct. Anal. Optim., 28, pp. 631-645
  • Dedieu, J.P., Points fixes (2006) zéros et la méthode de Newton, 54. , Springer, Berlin
  • Ezquerro, J.A., Gutiérrez, J.M., Hernández, M.A., Romero, N., Rubio, M.J., The Newton method: from Newton to Kantorovich (2010) (Spanish) Gac. R. Soc. Math. Esp., 13, pp. 53-76
  • Kantorovich, L.V., Akilov, G.P., (1982) Functional Analysis, , Pergamon Press, Oxford
  • Ortega, L.M., Rheinboldt, W.C., (1970) Iterative Solution of Nonlinear Equations in Several Variables, , Academic press, New York
  • Proinov, P.D., New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems (2010) J. Complex., 26, pp. 3-42
  • Rheinboldt, W.C., On a theorem of S. Smale about Newton’s method for analytic mappings (1988) Appl. Math. Lett., 1, pp. 3-42
  • Shen, W., Li, C., Smale’s α-theory for inexact Newton methods under the γ-condition (2010) J. Math. Anal. Appl., 369, pp. 29-42
  • Smale, S., (1986) Newton’s Method Estimates from Data at One Point. The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics (Laramie, Wyo., 1985), pp. 185–196, , Springer, New York
  • Smale, S., (1987) Algorithms for solving equations. Proceedings of the International Congress of Mathematicians, (Berkeley, Calif., 1986), vol. 1–2, pp, , Am. Math. Soc., Providence, RI
  • Wang, D.R., Zhao, F.G., The theory of Smale’s point estimation and its applications, Linear/nonlinear iterative methods and verification of solution (Matsuyama, 1993) (1995) J. Comput. Appl. Math., 60, pp. 253-269
  • Wang, X.H., Convergence of Newton’s method and inverse function theorem in Banach space (1999) Math. Comput., 68, pp. 169-186
  • Yakoubsohn, J.C., Finding zeros of analytic functions: α–theory for Secant type method (1999) J. Complex., 15, pp. 239-281
  • Zabrejko, P.P., Nguen, D.F., The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates (1987) Numer. Funct. Anal. Optim., 9, pp. 671-684