CRPC-TR98761 August 1998 Title: On the Component-wise Convergence Rate Authors: Amr El-Bakry and Trond Steihaug Submitted August 1998; Available as Rice CAAM TR 98-16 Abstract: In this paper we investigate the convergence rate of a sequence of vectors provided that the convergence rates of the components are known. The result of this investigation is then used to study the m-step convergence rate of sequences. ------------------------------------------------------------------------------ Amr El-Bakry Computational and Applied Mathematics Rice University elbakry@caam.rice.edu Trond Steihaug Department of Informatics University of Bergen trond.steihaug@ii.uib.no