An introduction to hierarchical matrices

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On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver (2011, methodology): “We can approximate a dense matrix F whose off-diagonal blocks have small numerical ranks by rank-structured matrices such as H-matrices (Hackbusch 1999; Hackbusch and Börm 2002; Hackbusch and Khoromskij 2000), H2-matrices (Börm et al.”
Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form (2005, methodology): “This method becomes ecien t for large-scale sparse Lyapunov equations only if klskADIm is much smaller than n. Note that if the matrices E and A have a particular structure for which the hierarchical matrix arithmetic can be used, then also the methods proposed in [40, 41 ] can be applied to comput”
Chebyshev interpolation for nonlinear eigenvalue problems (2012, methodology): “To capture the 6 smallest distinct eigenvalues (17, counting multiplicities), we select [5,12] as the interval of interest.”
Fast Fourier Transform (2011, background): “Taylor expansion [71, 75, 73] and polynomial interpolation [72].”