Super-quadratic convergence in Aitken Delta(2) process

摘要

In this short note, the existence of a super-quadratic convergence sequence in the Aitken Delta(2) process is shown, when the original sequence is generated by the fixed-point iteration with the iteration function of the form T(x) = (r x + s)/(px + q), where p, q, r and s are constants satisfying ps - qr not equal 0 and p not equal 0.