Maximal order for multipoint methods with memory using hermitian information

Abstract

This paper considers multipoint iterations with memory for finding the root of the nonlinear equation f(x)= 0. Suppose that such an iteration uses multipoint Hermitian information (with memory m) and n new evaluations per iteration. We show that its order cannot exceed 2ⁿ, verifying a conjecture of Traub and Wozniakowski for the Hermitian case. This bound is shown to be sharp, by exhibiting a class of methods whose order monotonically approaches 2ⁿ as m increases to infinity.

Keywords:

• Multipoint methods
• non-linear equation
• memory
• maximal order
• hermitian information

C.R. Categories:

• 5.15