Averaged Adaptive Cross Approximation for Structured Matrices

A modified form of the adaptive cross approximation (ACA) is considered for certain structured matrices for which the original ACA fails to provide controllably accurate matrix representations of low-rank submatrices. The modified ACA algorithm considered here is based on forming an averaged matrix, obtained via left- and right- multiplication of the original matrix block by sparse matrices that have LU factorizations. The performance of the modified ACA algorithm is examined for several sub-matrices for which the original ACA fails to provide controllably accurate representations, and significantly improved error control is observed.