μ-faster convergence and μ-acceleration of convergence by regular matrices

Abstract

A new, nonclassical convergence acceleration concept, called -acceleration of convergence (where is a positive monotonically increasing sequence), is introduced and compared with the classical convergence acceleration concept. Regular matrix methods are used to accelerate the convergence of sequences. Kornfeld (J. Comput. Appl. Math., 1994, 53, 309-321) proved that if B-transform of every convergent sequence x converges not slower than its A-transform, where A and B are regular matrix methods, then A and B are equivalent. In this paper it is proved that Kornfeld's assertion cannot be transferred to -acceleration of convergence in a general case.