Local convergence of a Newton–Traub composition in Banach spaces

Amat, S., Busquier, S., Plaza, S.: Dynamics of the King and Jarratt iterations. Aequationes Math. 69, 212–223 (2005)

Amat, S., Busquier, S., Plaza, S.: Chaotic dynamics of a third-order Newton-type method. J. Math. Anal. Appl. 366, 24–32 (2010)

Amat, S., Hernández, M.A., Romero, N.: A modified Chebyshev’s iterative method with at least sixth order of convergence. Appl. Math. Comput. 206, 164–174 (2008)

Argyros, I.K.: Convergence and Applications of Newton-type Iterations. Springer, New York (2008)

Argyros, I.K., Magreñán, Á.A.: Ball convergence theorems and the convergence planes of an iterative methods for nonlinear equations. SeMa 71, 39–55 (2015)

Candela, V., Marquina, A.: Recurrence relations for rational cubic methods I: the Halley method. Computing 44, 169–184 (1990)

Chun, C.: Some improvements of Jarratt’s method with sixth-order convergence. Appl. Math. Comput. 190, 1432–1437 (2007)

Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 199, 686–698 (2007)

Cordero, A., Ezquerro, J.A., Hernández-Veron, M.A., Torregrosa, J.R.: On the local convergence of a fifth-order iterative method in Banach spaces. Appl. Math. Comput. 251, 396–403 (2015)

Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia (1996)

Ezquerro, J.A., Hernández, M.A.: New iterations of R-order four with reduced computational cost. BIT Numer. Math. 49, 325–342 (2009)

Grau-Sánchez, M., Noguera, M., Gutiérrez, J.M.: On some computational orders of convergence. Appl. Math. Lett. 23, 472–478 (2010)

Herceg, D., Herceg, D.J.: Means based modifications of Newtons method for solving nonlinear equations. Appl. Math. Comput. 219, 6126–6133 (2013)

Homeier, H.H.H.: On Newton-type methods with cubic convergence. J. Comput. Appl. Math. 176, 425–432 (2005)

Hernández, M.A., Martínez, E.: On the semilocal convergence of a three steps Newton-type process under mild convergence conditions. Numer. Algorithms 70, 377–392 (2015)

Hernández, M.A.: Chebyshev’s approximation algorithms and applications. Comput. Math. Appl. 41, 433–455 (2001)

Jarratt, P.: Some fourth order multipoint methods for solving equations. Math. Comput. 20, 434–437 (1966)

Kou, J.: A third-order modification of Newton method for system of nonlinear equation. Appl. Math. Comput. 191, 117–121 (2007)

Kou, J., Li, Y., Wang, X.: Third-order modification of Newton’s method. J. Comput. Appl. Math. 205, 1–5 (2007)

Li, D., Liu, P., Kou, J.: An improvement of the Chebyshev–Halley methods free from second derivative. Appl. Math. Comput. 235, 221–225 (2014)

Lukić, T., Ralević, N.M.: Geometric mean Newton’s method for simple and multiple roots. Appl. Math. Lett. 21, 30–36 (2008)

Neta, B.: A sixth order family of methods for nonlinear equations. Int. J. Comput. Math. 7, 157–161 (1979)

Özban, A.Y.: Some new variants of Newton’s method. Appl. Math. Lett. 17, 677–682 (2004)

Parhi, S.K., Gupta, D.K.: Recurrence relations for a Newton-like method in Banach spaces. J. Comput. Appl. Math. 206, 873–887 (2007)

Parhi, S.K., Gupta, D.K.: A sixth order method for nonlinear equations. Appl. Math. Comput. 203, 50–55 (2008)

Ren, H., Wu, Q., Bi, W.: New variants of Jarratt’s method with sixth-order convergence. Numer. Algorithms 52, 585–603 (2009)

Rheinboldt, W.C.: An adaptive continuation process for solving systems of nonlinear equations. Polish Acad. Sci. Banach Center Publ. 3, 129–142 (1979)

Sharma, J.R., Guha, R.K., Sharma, R.: An efficient fourth-order weighted-Newton method for system of nonlinear equations. Numer. Algorithms 62, 307–323 (2013)

Sharma, J.R., Sharma, R., Bahl, A.: An improved Newton–Traub composition for solving systems of nonlinear equations. Appl. Math. Comput. 290, 98–110 (2016)

Traub, J.F.: Iterative Methods for the Solution of Equations. Chelsea Publishing Company, New York (1982)

Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third order convergence. Appl. Math. Lett. 13, 87–93 (2000)

Zhou, X.: A class of Newton’s methods with third-order convergence. Appl. Math. Lett. 20, 1026–1030 (2007)