  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.
