Generalized augmented matrix preconditioning approach and its application to iterative solution of ill-conditioned algebraic systems (Q2706289)

As a generalization of the augmented matrix preconditioning approach, a new preconditioning technique is introduced. The developed preconditioners are able to improve significantly an eigenvalue distribution of certain several ill-conditioned systems. Instead of ``deflating'' the small eigenvalues, these preconditioners propose to ``move'' them to the vicinity of the largest eigenvalue. The developed algorithm belongs to the additive Schwarz framework. One of the main advantages of the proposed approach is the possibility of using inexact solvers within the projectors.