Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling

The accuracy of the Adaptive Cross Approximation (ACA) algorithm, a popular method for the compression of low rank matrix blocks in Method of Moment computations, is sometimes seriously compromised by unpredictable errors in the convergence criterion. This paper proposes an alternative criterion, based on global sampling of the error in the elements of the ACA compressed matrix. The sampling error depends on the size of the sample but also on the population distribution of the error, which makes it difficult to control the error independently of the underlying problem. However, as argued and demonstrated in the paper, the distribution of the error converges to the same unique probability distribution function for all low rank matrices. Complementing the sampling criterion with a simple mechanism to detect this convergence, we arrive at a criterion that controls the error irrespective of the underlying problem. As a practical example the RCS of a moderate size metallic ogive is computed to illustrate the merits of the proposed criterion. The proposed algorithm may also be useful in other methods that approximate low-rank matrices by interpolation of a reduced set of its elements.
This work was partly funded by the Ministerio de Ciencia e Innovacion (MICINN) under projects TEC2016-78028-C3-1-P, TEC2017-84817-C2-2-R, TEC2017-83343-C4-2-R, PID 2019-107885GBC31, MDM2016-0600, and Catalan Research Group 2017 SGR 219.
Peer Reviewed
Postprint (author's final draft)