  In this paper we make a theoretical analysis of the convergence rates of
Kaczmarz and Extended Kaczmarz projection algorithms for some of the most
practically used control sequences. We first prove an at least linear
convergence rate for the Kaczmarz-Tanabe and its Extended version methods (the
one in which a complete set of projections using row/column index is performed
in each iteration). Then we apply the main ideas of this analysis in
establishing an at least sublinear, respectively linear convergence rate for
the Kaczmarz algorithm with almost cyclic and the remotest set control
strategies, and their extended versions, respectively. These results complete
the existing ones related to the random selection procedures.
