Aleksandrov, L.: The Newton-Kantorovich regularized computing processes. USSR Comput. Math. Math. Phys. 11(1), 46–57 (1971)
Amat, S., Busquier, S.: On a higher order secant method. Appl. Math. Comput. 141(2–3), 321–329 (2003)
Amat, S., Busquier, S., Magreñan, A.A.: Reducing chaos and bifurcations in Newton-type methods. Abstr. Appl. Anal. 726701, 10 (2013)
[+]
Aleksandrov, L.: The Newton-Kantorovich regularized computing processes. USSR Comput. Math. Math. Phys. 11(1), 46–57 (1971)
Amat, S., Busquier, S.: On a higher order secant method. Appl. Math. Comput. 141(2–3), 321–329 (2003)
Amat, S., Busquier, S., Magreñan, A.A.: Reducing chaos and bifurcations in Newton-type methods. Abstr. Appl. Anal. 726701, 10 (2013)
Argyros, I.K., Hilout, S.: On the semilocal convergence of damped Newton’s method. Appl. Math. Comput. 219, 2808–2824 (2012)
Argyros, I.K., Gutiérrez, J.M., Magreñán, Á.A., Romero, N.: Convergence of the relaxed Newton’s method. J. Korean. Math. Soc. 51(1), 137–162 (2014)
Babajee, D.K.R., Cordero, A., Soleymani, F., Torregrosa, J.R.: On improved three-step schemes with high efficiency index and their dynamics. Numer. Algorithms 65, 153–169 (2014)
Cordero, A., Lotfi, T., Mahdiani, K., Torregrosa, J.R.: Two optimal general classes of iterative methods with eight-order. Acta Appl. Math. doi: 10.1007/s10440-014-9869-0
Cordero, A., Torregrosa, J.R.: A class of Steffensen type methods with optimal order of convergence. Appl. Math. Comput. 217, 7653–7659 (2011)
Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact newton methods. SIAM J. Numer. Anal. 19, 400–408 (1982)
Dennis, J.E., Jr. Schnabel, R.B.: Numerical methods for unconstrained optimization and nonlinear equations. Classics in applied mathematics, vol. 16. SIAM (1996)
Ermakov, V.V., Kalitkin, N.N.: The optimal step and regularization for Newton’s method. USSR Comput. Math. Math. Phys. 21(2), 235–242 (1981)
Ezquerro, J.A., Hernández, M.A., Romero, N.: On some one-point hybrid iterative methods. Original Res. Art. Nonlinear Anal. Theory Methods Appl. 72(2), 587–601 (2010)
Gavurin, M.K.: Nonlinear functional equations and continuous analogues of iteration methods. Izvestiya Vysshikh Uchebnykh Zavedenii Matematika 5, 18–31 (1958)
Hernández, M.A., Romero, N.: A uniparametric family of iterative processes for solving nondifferentiable equations. J. Math. Annal. Appl. 275, 821–834 (2002)
Kalitkin, N.N., et al.: Mathematical Models in Nature and Science. Moscow (2005, in Russian)
Kalitkin, N.N., Poshivailo, I.P.: Computation of simple and multiple roots of a nonlinear equation. Math. Models Comput. Simul. 1(4), 514–520 (2009)
Kalitkin, N.N., Kuz’mina, L.V.: Computation of roots of an equation and determination of their multiplicity. Math. Models Comput. Simul. 3(1), 65–80 (2011)
Kung, H.T., Traub, J.F.: Optimal order of one-point and multi-point iteration. J. Assoc. Comput. Mach. 21, 643–651 (1974)
Madorskij, V.M.: Quasi-Newtonian Processes for Solving Nonlinear Equations. Brest State University, Brest (2005, in Russian)
Magreñán, Á.A.: Estudio de la dinámica del método de Newton amortiguado. PhD Thesis University of La Rioja, Spain. http://dialnet.unirioja.es/servlet/tesis?codigo=38821 (2013)
More, J.J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization software. ACM Trans. Math. Softw. 7(1), 17–41 (1981)
Ostrowski, A.M.: Solutions of Equations and Systems of Equations. Academic Press, New York-London (1966)
Puzynin, I.V., Zhanlav, T.: Convergence of iterations on the basis of a continuous analogue of the Newton method. Comput. Math. Math. Phys. 32(6), 729–737 (1992)
Puzynin, I.V., et al.: The generalized continuous analog of Newton’s method for the numerical study of some nonlinear quantum-field models. Phys. Part. Nucl. 30, 87 (1999)
Tikhonov, A.N.: Regularization of incorrectly posed problems. Soviet Math. Dokl. 4, 6 (1963)
Tikhonov, A.N.: The stability of algorithms for the solution of degenerate systems of linear algebraic equations. USSR Comput. Math. Math. Phys. 5(4), 181–188 (1965)
Tikhonov, A.N., Arsenin, V.Y.: Methods for Solving Ill-Posed Problems. John Wiley and Sons Inc, New York (1977)
Velasco Del Olmo, A.I.: Mejoras de los dominios de puntos de salida de métodos iterativos que no utilizan derivadas. PhD University of La Rioja, Spain. http://dialnet.unirioja.es/servlet/tesis?codigo=38218 (2013)
Ypma, T.J.: Local convergence of inexact Newton methods. SIAM J. Numer. Anal. 21, 583–590 (1984)
Zhidkov, E.P., Makarenko, G.J., Puzynin, I.V.: Continuous analogue of Newton’s method in nonlinear problems of physics. Phys. Part. Nuclei. 4(1), 127–166 (1973). (in Russian)
[-]