Abstract
We consider a one parameter family of iteration methods for finding zeros of algebraic equations. The family includes the second order Newton-Raphson's, third order Halley's and modified Newton-Raphson's methods. Investigation of the relationship between the number of iteration times and the parameter value reveals that the computational efficiency of the iteration methods should be evaluate in terms of the global behavior of the methods. The conclusion obtained are also applicable to other one parameter families, such as the one introduced by E. Hansen and M.Patrick. Numerical examples are included.
