The stationary iterations revisited

Abstract

In this paper, we first present a necessary and sufficient conditions for the weakly and strongly convergence of the general stationary iterations $x^{(k+1)} = T x^{(k)} +c$ with initial iteration matrix $T$ and vectors $c$ and $x^{(0)}$. Then we apply these general results and present convergence conditions for the stationary iterations for solving singular linear system $A x = b$. We show that our convergence conditions are weaker and more general than the known results.