A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics. (9th December 2015) - Fernández-Torres, Gustavo
Abstract : A geometric modification to the Newton-Secant method to obtain the root of a nonlinear equation is described and analyzed. With the same number of evaluations, the modified method converges faster than Newton's method and the convergence order of the new method is1 + 2 ≈ 2.4142 . The numerical examples and the dynamical analysis show that the new method is robust and converges to the root in many cases where Newton's method and other recently published methods fail.