Abstract

Newton's method to find the zero of a function in one variable uses the ratio of the function and derivative values, but it does not use the information provided by these quantities separately. It is a natural question to ask what a method would look like that does take into account these values instead of just their ratio. We answer that question in the case of a polynomial with all real zeros, the result being a method that is somewhat reminiscent of Laguerre's method.

Keywords: Newton; Laguerre; polynomial; zero; root.

MSC: 65H04

Pages:  295$-$304     

Volume  63 ,  Issue  3 ,  2011