Numerical Methods for Roots of Polynomials - Part II

9.9.2 Methods Using Inverse Interpolation

The interpolatory methods referred to above are hard to implement if the degree of is greater than 2 or 3. In many ways inverse interpolation is easier to implement, and several authors describe methods based on this process. For example consider Traub (1962): let have an inverse function , then he shows that

(9.735)

where as usual ,

(9.736)

(9.737)

and where for the inner sum is taken over all such ...