Some variant of Newton's method with third-order convergence

By Marco Frontini, E. Sormani. Applied Mathematics and Computation, 2003

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Review of some iterative root-finding methods from a dynamical point of view (2004, methodology): “These three third{order root{flnding iterative methods are studied in [ 25 ], [41], [45], [59].”
New iterations of R-order four with reduced computational cost (2009, methodology): “For example, in [ 6 , 8, 9], we can see Newtontype methods for rootfinding with cubic convergence.”
Recurrence relations for a Newton-like method in Banach spaces (2007, background): “[6] M. Frontini, E. Sormani, Third-order methods from quadrature formulae for solving systems of nonlinear equations, Appl.”