Some sixth order zero-finding variants of Chebyshev–Halley methods

摘要

A zero-finding technique in which the order of convergence is improved and nonlinear equations are solved more efficiently than they are solved by traditional iterative methods is derived. Composing a modified Chebyshev–Halley method with a variant of this method that just introduces one evaluation of the function the iterative methods presented are obtained. By carrying out this procedure the output numerical results show that the new methods compete in both order and efficiency with the modified Chebyshev–Halley methods.