For symmetric multiple saddle-point systems with any number of blocks, the eigenvalues of the block-diagonally preconditioned matrix lie in computable intervals that depend only on the number of blocks.
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Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices
For symmetric multiple saddle-point systems with any number of blocks, the eigenvalues of the block-diagonally preconditioned matrix lie in computable intervals that depend only on the number of blocks.