Enlarging The convergence domain of secant-like methods for equations

Autor: Argyros, I.K.; Ezquerro Fernández, José AntonioHernández Verón, Miguel Angel; Hilout, S.; Magreñan, A.A.; 

Tipo de documento: Artículo de revista

Revista: Taiwanese Journal of Mathematics. ISSN: 1027-5487. Año: 2015. Número: 2. Volumen: 19. Páginas: 629-652.

doi 10.11650/tjm.19.2015.4404Texto completo open access 

SCIMAGO (datos correspondientes al año 2014):
,547  SNIP: ,868 



  • Amat, S., Busquier, S., Negra, M., Adaptive approximation of nonlinear operators (2004) Numer. Funct. Anal. Optim., 25, pp. 397-405
  • Amat, S., Busquier, S., Gutiérrez, J.M., On the local convergence of secant-type methods (2004) International Journal of Computer Mathematics, 81 (8), p. 7
  • Amat, S., Bermúdez, C., Busquier, S., Gretay, J.O., Convergence by nondiscrete mathematical induction of a two step secant's method (2007) Rocky Mountain Journal of Mathematics, 37 (2), p. 7
  • Andronow, A.A., Chaikin, C.E., (1949) Theory of Oscillations, , Princenton University Press, New Jersey
  • Argyros, I.K., (1998) Polynomial Operator Equations in Abstract Spaces and Applications, , St.Lucie/CRC/Lewis Publ. Mathematics series, Boca Raton, Florida, U.S.A
  • Argyros, I.K., A unifying local-semilocal convergence analysis and applications for twopoint Newton-like methods in Banach space (2004) J. Math. Anal. Appl., 298, pp. 374-397
  • Argyros, I.K., New sufficient convergence conditions for the secant method (2005) Chechoslovak Math. J., 55, pp. 175-187
  • Argyros, I.K., (2008) Convergence and Applications of Newton-type Iterations, , Springer-Verlag Publ., New-York
  • Argyros, I.K., A semilocal convergence analysis for directional Newton methods (2011) Math. Comput., 80, pp. 327-343
  • Argyros, I.K., Cho, Y.J., Hilout, S., (2012) Numerical Methods for Equations and Its Applications, , CRC Press/Taylor and Francis, Boca Raton, Florida, USA
  • Argyros, I.K., Hilout, S., Convergence conditions for secant-type methods (2010) Chechoslovak Math. J., 60, pp. 253-272
  • Argyros, I.K., Hilout, S., Weaker conditions for the convergence of Newton's method (2012) J. Complexity, 28, pp. 364-387
  • Argyros, I.K., Hilout, S., Estimating upper bounds on the limit points of majorizing sequences for Newton's method (2013) Numer. Algorithms, 62 (1), p. 7
  • Argyros, I.K., Hilout, S., (2013) Numerical Methods in Nonlinear Analysis, , World Scientific Publ. Comp., New Jersey
  • Argyros, I.K., Ezquerro, J.A., Hernańdez, M.Á., Hilout, S., Romero, N., Velasco, A.I., Expanding the applicability of secant-like methods for solving nonlinear equations, , submitted for publications
  • Dennis, J.E., Toward a unified convergence theory for Newton-like methods (1971) Nonlinear Functional Analysis and Applications, pp. 425-472. , (L. B. Rall, ed.), Academic Press, New York
  • Ezquerro, J.A., Gutiérrez, J.M., Hernández, M.A., Romero, N., Rubio, M.J., The Newton method: From Newton to Kantorovich, (Spanish) (2010) Gac. R. Soc. Mat. Esp., 13, pp. 53-76
  • Ezquerro, J.M., Hernández, M.A., Romero, N., Velasco, A.I., (2012) Improving the domain of starting point for secant-like methods, 219 (8), pp. 3677-3692
  • Ezquerro, J.A., Rubio, M.J., A uniparametric family of iterative processes for solving nondifferentiable equations (2002) J. Math. Anal. Appl., 275, pp. 821-834
  • Hernández, M.A., Rubio, M.J., Ezquerro, J.A., Secant-like methods for solving nonlinear integral equations of the Hammerstein type. Proceedings of the 8th International Congress on Computational and Applied Mathematics, ICCAM-98 (Leuven) (2000) J. Comput. Appl. Math., 115, pp. 245-254
  • Hernández, M.A., Rubio, M.J., Ezquerro, J.A., Solving a special case of conservative problems by secant-like methods (2005) Appl. Math. Comput., 169, pp. 926-942
  • Kantorovich, L.V., Akilov, G.P., (1982) Functional Analysis, , Pergamon Press, Oxford
  • Laasonen, P., Ein überquadratisch konvergenter iterativer algorithmus (1969) Ann. Acad. Sci. Fenn. Ser I, 450, pp. 1-10
  • Ortega, J.M., Rheinboldt, W.C., (1970) Iterative Solution of Nonlinear Equations in Several Variables, , Academic Press, New York
  • Potra, F.A., Sharp error bounds for a class of Newton-like methods (1985) Libertas Mathematica, 5, pp. 71-84
  • Potra, F.A., Pták, V., (1984) Nondiscrete Induction and Iterative Processes, , Pitman, New York
  • Proinov, P.D., General local convergence theory for a class of iterative processes and its applications to Newton's method (2009) J. Complexity, 25, pp. 38-62
  • Proinov, P.D., New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems (2010) J. Complexity, 26, pp. 3-42
  • Schmidt, J.W., Untere Fehlerschranken fur Regula-Falsi Verhafren (1978) Period. Hungar., 9, pp. 241-247
  • Stoker, J.J., (1950) Nonlinear Vibrations, , Interscience-Wiley, New York
  • Traub, J.F., (1964) Iterative Methods for the Solution of Equations, , Prentice-Hall, Englewood Cliffs, New Jersay
  • Yamamoto, T., A convergence theorem for Newton-like methods in Banach spaces (1987) Numer. Math., 51, pp. 545-557
  • Wolfe, M.A., Extended iterative methods for the solution of operator equations (1978) Numer. Math., 31, pp. 153-174