A new cubic method for computing a root

Abstract

In this paper a new cubic order root finding method is introduced. The algorithm can be used to find a simple root in an interval I of f(x)=0 where the function is convex. The method is a hybrid procedure that combines Newton's quadratic root finding method with a superlinear method. The new procedure requires only one first derivative evaluation per application of the method Newton's cubic root finding method is also described for comparison purposes. It requires the evaluation of the function and its first and second derivatives at each iteration. Another cubic method that combines a Steffensen-type method with the secant method will be discussed as well along with a modified version of this procedure. A table of numerical results is presented to compare the methods.

Keywords:

• Simple Root
• Newton Cubic Order Method
• Asymptotic Convergence

C.R. Categories:

• G 1.5

^†Supported by NSERC.

^†Supported by NSERC.

Notes

^†Supported by NSERC.