Modified Newton's method with third-order convergence and multiple roots

By M. Frontini, E. Sormani. 2003

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On Newton-type methods with cubic convergence (2005, background): “Frontini and Sormani [4,5] considered the midpoint rule ∫ x”
Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations (2010, background): “A large number of papers have been written about iterative methods for the solution of the the nonlinear equations [3] [7] [8] [9] [10] [12] [13].”
Modified Newton's method for systems of nonlinear equations with singular Jacobian (2009, unknown): “In recent papers (see [2] [5]) methods for acceleration of iterative processes for solving a nonlinear equation with multiple roots have been presented.”