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.

中文翻译：

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一种并行分层分块自适应交叉逼近算法

本文提出了一种基于矩阵项子采样的低秩分解算法。所提出的算法首先使用分块自适应交叉逼近 (BACA) 算法计算子矩阵的秩揭示分解，然后通过截断奇异值分解 (H-BACA) 应用分层合并操作。所提出的算法显着提高了基线 ACA 算法的收敛性，与传统的分解（如秩显示 QR）相比，降低了计算复杂度。数值结果证明了所提出算法的效率、准确性和并行可扩展性。