Increasing the order of convergence for iterative methods to solve nonlinear systems

Amat, S., Busquier, S., Gutiérrez, J.M.: Geometrical constructions of iterative functions to solve nonlinear equations. J. Comput. Appl. Math. 157, 197–205 (2003)

Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: Increasing the convergence order of an iterative method for nonlinear systems. Appl. Math. Lett. 25, 2369–2374 (2012)

Cordero, A., Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007)

Darvishi, M.T., Barati, A.: A fourth-order method from quadrature formulae to solve systems of nonlinear equations. Appl. Math. Comput. 188, 257–261 (2007)

Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P., Zimmermann, P.: MPFR: a multiple-precision binary floating-point library with correct rounding. ACM Trans. Math. Software 33(2), 15. Art. 13 (2007)

Frontini, M., Sormani, E.: Some variant of Newton’s method with third-order convergence. Appl. Math. Comput. 140, 419–426 (2003)

Frontini, M., Sormani, E.: Third-order methods from quadrature formulae for solving systems of nonlinear equations. Appl. Math. Comput. 149, 771–782 (2004)

Grau-Sánchez, M., Grau, A., Noguera, M.: Frozen divided difference scheme for solving systems of nonlinear equations. J. Comput. Appl. Math. 235, 1739–1743 (2011)

Grau-Sánchez, M., Grau, A., Noguera, M.: On the computational efficiency index and some iterative methods for solving systems of nonlinear equations. J. Comput. Appl. Math. 236, 1259–1266 (2011)

Grau-Sánchez, M., Grau, A., Noguera, M.: Ostrowski type methods for solving systems of nonlinear equations. Appl. Math. Comput. 218, 2377–2385 (2011)

Gutiérrez, J.M., Hernández, M.A.: A family of Chebyshev-Halley type methods in Banach spaces. Bull. Aust. Math. Soc. 55, 113–130 (1997)

Homeier, H.H.H.: A modified Newton method with cubic convergence: the multivariable case. J. Comput. Appl. Math. 169, 161–169 (2004)

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

Kelley, C.T.: Solving nonlinear equations with Newton’s method. SIAM, Philadelphia (2003)

Kou, J., Li, Y., Wang, X.: Some modification of Newton’s method with fifth-order convergence. J. Comput. Appl. Math. 209, 146–152 (2007)

Noor, M.A., Waseem, M.: Some iterative methods for solving a system of nonlinear equations. Comput. Math. Appl. 57, 101–106 (2009)

Ortega, J.M., Rheinboldt, W.C.: Iterative solutions of nonlinear equations in several variables. Academic Press, New York (1970)

Ostrowski, A.M.: Solution of equations and systems of equations. Academic Press, New York (1966)

Palacios, M.: Kepler equation and accelerated Newton method. J. Comput. Appl. Math. 138, 335–346 (2002)

Sharma, J.R., Arora, H.: Efficient Jarratt-like methods for solving systems of nonlinear equations. Calcolo 51, 193–210 (2014)

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

Sharma, J.R., Gupta, P.: An efficient fifth order method for solving systems of nonlinear equations. Comput. Math. Appl. 67, 591–601 (2014)

Xiao, X.Y., Yin, H.W.: A new class of methods with higher order of convergence for solving systems of nonlinear equations. Appl. Math. Comput. 264, 300–309 (2015)

Xiao, X.Y., Yin, H.W.: A simple and efficient method with high order convergence for solving systems of nonlinear equations. Comput. Math. Appl. 69, 1220–1231 (2015)