  This paper presents a hierarchical low-rank decomposition algorithm assuming
any matrix element can be computed in $O(1)$ time. The proposed algorithm
computes rank-revealing decompositions of sub-matrices with a blocked adaptive
cross approximation (BACA) algorithm, followed by a hierarchical merge
operation via truncated singular value decompositions (H-BACA). The proposed
algorithm significantly improves the convergence of the baseline ACA algorithm
and achieves reduced computational complexity compared to the full
decompositions such as rank-revealing QR decompositions. Numerical results
demonstrate the efficiency, accuracy and parallel efficiency of the proposed
algorithm.
