Linear convergence for vector sequences and some applications

AbstractIn this paper we first give the relation between some definitions of linearly convergent vector sequences proposed by Nievergelt, Osada and Sadok, and we choose the first one in order to generalize a theorem which gives the relation between the asymptotic behaviour of the ratios of the errors and that of the differences for linear convergent scalar sequences. Some properties of the matrix used in the definition of linear convergence are studied, and a convergence acceleration result which generalizes some results given by Nievergelt and Sadok is given