A note on the convergence of the Muller-Bisection method for solving nonlinear equations

In this note we present the convergence of the Muller-Bisectionmethod for solving nonlinear equations [Xinyuan Wu, ImprovedMuller method and Bisection method with global and asymptoticsuperlinear convergence of both point and interval for solvingnonlinear equations, Appl. Math. Comput. 166 (2005) 299-311]. Itis proven that the method can reach cubic convergence and notconvergence superlineal like Xinyuan proposes. The numericalcomparison with other methods with a cost of equal or superiorcalculation leaves evidence of the theoretical result.