Newton and Steffensen Type Methods with Flexible Order of Convergence

Abstract

New families of Newton and Steffensen type methods are derived by amalgamating known methods. The methods in the new families are of higher order than the methods amalgamated. The technique shows that it is possible to develop methods of any desired order.

Key words and phrases. Newton method, secant method, Steffensen method, order of convergence, derivative free method.

1991 Mathematics Subject Classification. 65H05