Levin, Y., Ben-Israel, A.: Directional Newton methods in n variables. Math. Comput. 71(237), 251–262 (2002)

Argyros, I.K., Hilout, S.: A convergence analysis for directional two-step Newton methods. Num. Algorithms 55(4), 503–528 (2010)

Lukács, G.: The generalized inverse matrix and the surface-surface intersection problem. In: Theory and Practice of Geometric Modeling, pp. 167–185. Springer (1989)
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Levin, Y., Ben-Israel, A.: Directional Newton methods in n variables. Math. Comput. 71(237), 251–262 (2002)

Argyros, I.K., Hilout, S.: A convergence analysis for directional two-step Newton methods. Num. Algorithms 55(4), 503–528 (2010)

Lukács, G.: The generalized inverse matrix and the surface-surface intersection problem. In: Theory and Practice of Geometric Modeling, pp. 167–185. Springer (1989)

Argyros, I.K., Magreñán, Á.A.: Extending the applicability of Gauss–Newton method for convex composite optimization on Riemannian manifolds. Appl. Math. Comput. 249, 453–467 (2014)

Argyros, I.K.: A semilocal convergence analysis for directional Newton methods. Math. Comput. 80(273), 327–343 (2011)

Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. SIAM (2000)

Argyros, I.K., Hilout, S.: Weaker conditions for the convergence of Newton’s method. J. Complex. 28(3), 364–387 (2012)

Argyros, I.K., Hilout, S.: On an improved convergence analysis of Newton’s method. Appl. Math. Comput. 225, 372–386 (2013)

Tapia, R.A.: The Kantorovich theorem for Newton’s method. Am. Math. Mon. 78(4), 389–392 (1971)

Argyros, I.K., George, S.: Local convergence for some high convergence order Newton-like methods with frozen derivatives. SeMA J. 70(1), 47–59 (2015)

Martínez, E., Singh, S., Hueso, J.L., Gupta, D.K.: Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces. Appl. Math. Comput. 281, 252–265 (2016)

Argyros, I.K., Behl, R. Motsa,S.S.: Ball convergence for a family of quadrature-based methods for solving equations in banach Space. Int. J. Comput. Methods, pp. 1750017 (2016)

Parhi, S.K., Gupta, D.K.: Convergence of Stirling’s method under weak differentiability condition. Math. Methods Appl. Sci. 34(2), 168–175 (2011)

Prashanth, M., Gupta, D.K.: A continuation method and its convergence for solving nonlinear equations in Banach spaces. Int. J. Comput. Methods 10(04), 1350021 (2013)

Parida, P.K., Gupta, D.K.: Recurrence relations for semilocal convergence of a Newton-like method in banach spaces. J. Math. Anal. Appl. 345(1), 350–361 (2008)

Argyros, I.K., Hilout, S.: Convergence of Directional Methods under mild differentiability and applications. Appl. Math. Comput. 217(21), 8731–8746 (2011)

Amat, S, Bermúdez, C., Hernández-Verón, M.A., Martínez, E.: On an efficient k-step iterative method for nonlinear equations. J. Comput. Appl. Math. 302, 258–271 (2016)

Hernández-Verón, M.A., Martínez, E., Teruel, C.: Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems. Num. Algorithms, pp. 1–23

Argyros, M., Hernández, I.K., Hilout, S., Romero, N.: Directional Chebyshev-type methods for solving equations. Math. Comput. 84(292), 815–830 (2015)

Davis, P.J., Rabinowitz, P.: Methods of numerical integration. Courier Corporation (2007)

Cordero, A, Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Computation . 190(1), 686–698 (2007)

Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13(8), 87–93 (2000)

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