Efficient Algorithms for CUR and Interpolative Matrix Decompositions

TL;DR

This paper introduces efficient algorithms for CUR and ID matrix decompositions, leveraging classical QR methods and randomized projections to improve performance and applicability in various computational scenarios.

Contribution

It presents novel modifications to QR-based algorithms and integrates randomized techniques, enabling faster and more scalable CUR and ID factorizations.

Findings

Algorithms outperform existing methods in speed and accuracy.

Randomized projections further accelerate computations.

Numerical experiments validate the efficiency gains.

Abstract

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for implementation. For certain applications, further acceleration can be attained by incorporating techniques based on randomized projections. Numerical experiments demonstrate advantageous performance compared to existing techniques for computing CUR factorizations.