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arXiv · 1901.06101

A Parallel Hierarchical Blocked Adaptive Cross Approximation Algorithm

Yang Liu·Wissam Sid-Lakhdar·Elizaveta Rebrova·Pieter Ghysels·Xiaoye Sherry Li
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Abstract

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.

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Yang Liu, Wissam Sid-Lakhdar, Elizaveta Rebrova, Pieter Ghysels, Xiaoye Sherry Li. 2019-01-18. A Parallel Hierarchical Blocked Adaptive Cross Approximation Algorithm. https://arxiv.org/abs/1901.06101

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