On the global convergence of Chebyshevʹs iterative method

In [A. Melman, Geometry and convergence of Eulerʹs and Halleyʹs methods, SIAM Rev. 39(4) (1997) 728–735] the geometry and global convergence of Eulerʹs and Halleyʹs methods was studied. Now we complete Melmanʹs paper by considering other classical third-order method: Chebyshevʹs method. By using the geometric interpretation of this method a global convergence theorem is performed. A comparison of the different hypothesis of convergence is also presented.