Two sides tangential filtering decomposition
Journal of Computational and Applied Mathematics
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Eigenvalue estimates of block incomplete preconditioners are considered. We investigate how the block diagonal entries and off-block diagonal entries influence the bounds of all eigenvalues. The results presented here improve and unify some previous results. We generalize the well-known inequality that the spectral radius is bounded by the trace for symmetric positive semidefinite matrices to block form. Some of the methods can also be useful to estimate lower bounds of block incomplete preconditioners.