Simple randomized strategies for low-rank matrix compression

We propose a randomized Pseudo Skeleton (or CUR) approximation method to compress the H-matrices of linear systems that arise in the discretization of integral equations in electromagnetic scattering. This method is essentially the Matrix Decomposition Algorithm (MDA) of Michielssen and Boag (1994) with equivalent basis and testing functions equal to a random subset of the original ones. It is highly parellelizable and well suited for fine-granularity architectures as GPUs. As the Adaptive Cross Approximation (ACA), CUR is purely algebraic. The method is tested with standard cases to assess its quality and efficiency.
This work was partly funded by the Ministerio de Ciencia e Innovacion (MICINN) under projects PID2019-107885GBC31 / AEI / 10.13039/501100011033, PID2022-136869NBC31 / AEI / 10.13039/501100011033, PID2020-113832RBC21 / AEI / 10.13039/501100011033 and PID-2020-118410RB-C21 / AEI / 10.13039/501100011033, PDC2022-133091-I00 / AEI / 10.13039/501100011033, and Catalan Research Group 2017 SGR 219 and grant 2021 FI B2 00096.
Peer Reviewed
Postprint (published version)