# Fast Randomized Matrix and Tensor Interpolative Decomposition Using CountSketch

## TL;DR

This paper introduces a fast randomized algorithm for matrix and tensor interpolative decomposition using CountSketch, offering significant speed improvements while maintaining accuracy, applicable to large-scale data.

## Contribution

The paper presents a novel CountSketch-based randomized algorithm for matrix and tensor interpolative decomposition with theoretical guarantees and improved computational efficiency.

## Key findings

- Achieves at least an order of magnitude speed-up on large matrices and tensors.
- Maintains accuracy comparable to existing methods.
- Provides theoretical performance guarantees for both matrix and tensor cases.

## Abstract

We propose a new fast randomized algorithm for interpolative decomposition of matrices which utilizes CountSketch. We then extend this approach to the tensor interpolative decomposition problem introduced by Biagioni et al. (J. Comput. Phys. 281, pp. 116-134, 2015). Theoretical performance guarantees are provided for both the matrix and tensor settings. Numerical experiments on both synthetic and real data demonstrate that our algorithms maintain the accuracy of competing methods, while running in less time, achieving at least an order of magnitude speed-up on large matrices and tensors.