We present block variants of the discrete empirical interpolation method (DEIM); as a particular application, we will consider a CUR factorization. The block DEIM algorithms are based on the concept of the maximum volume of submatrices and a rank-revealing QR factorization. We also present a version of the block DEIM procedures, which allows for adaptive choice of block size. The results of the experiments indicate that the block DEIM algorithms exhibit comparable accuracy for low-rank matrix approximation compared to the standard DEIM procedure. However, the block DEIM algorithms also demonstrate potential computational advantages, showcasing increased efficiency in terms of computational time.

翻译：本文提出了离散经验插值方法（DEIM）的块化变体；作为一种具体应用，我们将考虑CUR分解。块DEIM算法基于子矩阵最大体积的概念和秩揭示QR分解。我们还提出了一种块DEIM流程的版本，允许自适应选择块大小。实验结果表明，在低秩矩阵近似方面，块DEIM算法与标准DEIM流程相比具有相当的精度。然而，块DEIM算法也展现出潜在的计算优势，在计算时间方面表现出更高的效率。