Block Discrete Empirical Interpolation Methods

TL;DR

This paper introduces block variants of the discrete empirical interpolation method (DEIM) that leverage maximum volume submatrices and QR factorizations, offering comparable accuracy and improved efficiency for low-rank matrix approximation.

Contribution

It develops novel block DEIM algorithms with adaptive block size selection, enhancing computational efficiency while maintaining accuracy.

Findings

Block DEIM achieves similar accuracy to standard DEIM.

Block DEIM demonstrates increased computational efficiency.

Algorithms are based on maximum volume submatrices and QR factorization.

Abstract

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.