A parallel hierarchical blocked adaptive cross approximation algorithm. (July 2020) - Liu, Yang; Sid-Lakhdar, Wissam; Rebrova, Elizaveta; Ghysels, Pieter; Li, Xiaoye Sherry
This article presents a low-rank decomposition algorithm based on subsampling of matrix entries. The proposed algorithm first computes rank-revealing decompositions of submatrices with a blocked adaptive cross approximation (BACA) algorithm, and then applies 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 traditional decompositions such as rank-revealing QR. Numerical results demonstrate the efficiency, accuracy, and parallel scalability of the proposed algorithm.