RandNLA: randomized numerical linear algebra Page 1 80 COMMUNICATIONS OF THE ACM
| JUNE 2016 | VOL. 59 | NO. 6 review articles DOI:10.1145/2842602 Randomization offers new …

Subsampling focuses on selecting a subsample that can efficiently sketch the information of
the original data in terms of statistical inference. It provides a powerful tool in big data …

This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

This survey highlights the recent advances in algorithms for numerical linear algebra that
have come from the technique of linear sketching, whereby given a matrix, one first …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

Since the early 1980. the first author has taught a graduate course in numerical linear
algebra at MIT and Cornell. The alumni of this course, now numbering in the hundreds, have …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

The statistical leverage scores of a matrix A are the squared row-norms of the matrix
containing its (top) left singular vectors and the coherence is the largest leverage score …

We reconsider randomized algorithms for the low-rank approximation of SPSD matrices
such as Laplacian and kernel matrices that arise in data analysis and machine learning …

The CANDECOMP/PARAFAC (CP) decomposition is a leading method for the analysis of
multiway data. The standard alternating least squares algorithm for the CP decomposition …