Sketch-and-project methods for tensor linear systems

TL;DR

This paper introduces sketch-and-project methods for solving tensor linear systems with the t-product, including adaptive variants and improved sampling strategies, demonstrating competitive convergence and efficiency in experiments.

Contribution

It proposes novel sketch-and-project algorithms for tensor systems, along with adaptive and improved sampling strategies, and provides convergence analysis and empirical comparisons.

Findings

Methods show competitive convergence rates.

Algorithms perform well in terms of iterations and runtime.

Effective in both synthetic and real data scenarios.

Abstract

For tensor linear systems with respect to the popular t-product, we first present the sketch-and-project method and its adaptive variants. Their Fourier domain versions are also investigated. Then, considering that the existing sketching tensor or way for sampling has some limitations, we propose two improved strategies. Convergence analyses for the methods mentioned above are provided. We compare our methods with the existing ones using synthetic and real data. Numerical results show that they have quite decent performance in terms of the number of iterations and running time.