n-Evaluation Conjecture for Multipoint Iterations for the Solution of Scalar Nonlinear Equations

Kung and Traub conjectured that any multipoint iteration without memory which uses n evaluations per iterative step has order of convergence no higher than 2. It is known that this conjecture is true for n --< 3 and for Hermite information. It is proved here that the Kung-Traub conjecture holds in a wider class of iterations. For example, it holds whenever the problem is well poised in the sense of Birkhoff complex interpolation.