# Streaming Low-Rank Matrix Approximation with an Application to Scientific Simulation

## TL;DR

This paper introduces a new streaming algorithm for low-rank matrix approximation that improves accuracy and robustness, enabling efficient compression of large scientific data sets with validated error estimates.

## Contribution

A novel streaming low-rank approximation algorithm with a priori analysis and a posteriori error estimator, enhancing accuracy and parameter robustness over prior methods.

## Key findings

- Achieves smaller relative approximation errors
- Less sensitive to parameter choices
- Effective in compressing scientific simulation data

## Abstract

This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm for constructing an accurate low-rank approximation of a matrix from streaming data. This method is accompanied by an a priori analysis that allows the user to set algorithm parameters with confidence and an a posteriori error estimator that allows the user to validate the quality of the reconstructed matrix. In comparison to previous techniques, the new method achieves smaller relative approximation errors and is less sensitive to parameter choices. As concrete applications, the paper outlines how the algorithm can be used to compress a Navier--Stokes simulation and a sea surface temperature dataset.