Stochastic Estimation of the Frobenius Norm in the ACA Convergence Criterion

The adaptive cross approximation (ACA) algorithm has been used in many fast Integral Equation solvers for electromagnetic Radiation and Scattering problems. It efficiently computes a low rank approximation to the interaction matrix between mutually distant parts of a scattering object. The ACA is an iterative algorithm that needs an accurate and efficient convergence criterion. The evaluation of this criterion may consume a considerable part of the computational resources. This communication presents an efficient new way to evaluate the convergence criterion, using a stochastic approach.