Optimizing $\mathcal{H}$-Matrix Solvers' Admissability Criteria via Rapid Spectrum Estimation

A recently introduced iterative random sampling algorithm is adopted to maximize the total compression of hierarchically partitioned impedance matrices by rapidly finding optimal admissibility criteria parameters (cluster-to-cluster distance measure, cluster-size measure, and admissibility constant) to set the block partition. Because the algorithm can estimate ranks accurately only for sufficiently incoherent matrix blocks, its rank estimates are penalized for blocks with relatively large size-to-distance ratios. The algorithm is tested on the PRIME aircraft model from the Austin RCS Benchmark Suite.