For Toeplitz-like matrices, the paper proves explicit epsilon-rank bounds of order rho log(m) log(1/epsilon) for off-diagonal submatrices of the transformed matrix and uses them to build adaptive HODLR and HSS compressors with guaranteed error.
Bebendorf, Hierarchical matrices, Springer, 2008
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Compression Properties for large Toeplitz-like matrices
For Toeplitz-like matrices, the paper proves explicit epsilon-rank bounds of order rho log(m) log(1/epsilon) for off-diagonal submatrices of the transformed matrix and uses them to build adaptive HODLR and HSS compressors with guaranteed error.