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