Mixed precision matrix interpolative decompositions for model reduction

TL;DR

This paper introduces a mixed-precision algorithm for matrix interpolative decomposition that achieves double-precision accuracy, leveraging GPU capabilities to improve efficiency in data-rich applications.

Contribution

The paper presents a novel mixed-precision algorithm for matrix interpolative decomposition that maintains high accuracy and demonstrates its effectiveness in model reduction tasks.

Findings

Viable approximation accuracy with low precision arithmetic.

Effective error estimates validated through numerical tests.

Successful application to model reduction in turbulent flow.

Abstract

Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose a mixed-precision algorithm to generate a double-precision accurate matrix interpolative decomposition approximation under a given set of criteria. Though low precision arithmetic suffers from quicker accumulation of round-off error, for many data-rich applications we nevertheless attain viable approximation accuracy, as the error incurred using low precision arithmetic is dominated by the error inherent to low-rank approximation. We then conduct several simulated numerical tests to demonstrate the efficacy of the algorithms and the corresponding error estimates. Finally, we present the application of our algorithms to a problem in model reduction for particle-laden turbulent flow.