A pseudo Laguerre method

Abstract

Newton's method to find the zero of a function in one variable usesthe ratio of the function and derivative values, but it does not usethe information provided by these quantities separately. It is anatural question to ask what a method would look like that does takeinto account these values instead of just their ratio. We answerthat question in the case of a polynomial with all real zeros, theresult being a method that is somewhat reminiscent of Laguerre'smethod.