A Scalable Binary CUR Low-Rank Approximation Algorithm

Low-rank matrix approximations are critical in large-scale data analysis, but classical methods like SVD and rank-revealing QR become computationally impractical for massive datasets. CUR decomposition offers an efficient alternative by selecting representative rows and columns, but identifying optimal sub-matrices-especially those with maximal volume-is NPhard and inherently sequential. In this work, we propose a novel Scalable Binary CUR Low-Rank Approximation Algorithm that leverages a Blockwise Adaptive Cross Approximation strategy to deterministically select informative rows and columns in parallel. By partitioning matrices into blocks and iteratively extracting dominant components using parallel norm-based selection and rank-1 updates, our method achieves high-quality CUR decompositions with significantly reduced runtime. Numerical experiments on synthetic and ill-conditioned matrices demonstrate both the accuracy and scalability of our algorithm, with speedups observed on multi-core architectures.