A Weighted Average Adaptive Cross Approximation

The adaptive cross approximation (ACA) is considered for matrix structures where error control is lost. A weighted average form of the ACA is presented that mitigates the loss of error control. In the averaged ACA (AACA) algorithm, the ACA is applied to a matrix comprising linear combinations of the rows and columns of the original matrix. An efficient implementation of the weighted average algorithm is outlined. The performance of the ACA and AACA are examined for both static and time-harmonic integral equation solutions of problems for which loss of error control by the ACA is observed. The behaviors of the ACA and AACA are compared and discussed, and the AACA is observed to maintain error control for many matrices for which the ACA fails.