Iteration Functions re-visited

摘要

Two classes of Iteration Functions (IFs) are derived in this paper. The first (one-point IFs) was originally derived by Joseph Traub using a different approach to ours (simultaneous IFs). The second is new and is demonstrably shown to be more informationally efficient than the first. These IFs apply to polynomials with arbitrary complex coefficients and zeros, which can also be multiple.