This contribution concerns the iterative solution of singular systems which arise in many applications. Let us mention the following: - solution of PDE problems with pure Neumann boundary conditions (which is our main aim), see [7], [8], [20]. Such problems have a specific role in numerical upscaling, see [6], - solution of Neumann type subproblems in domain decomposition techniques as FETI, Neumann-Neumann, BDDC methods, see [22], [16], - analysis of Markov chain problems, computation of stochastic vector, see e.g. [18], [19], - computer tomography [15], [14] and inverse problems [4], [21].
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