Low rank approximation of matrices has been well studied in literature. Singular value
decomposition, QR decomposition with column pivoting, rank revealing QR factorization …

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 numerical linear algebra-RandNLA, for short-concerns the use of
randomization as a resource to develop improved algorithms for large-scale linear algebra …

We show how to approximate a data matrix A with a much smaller sketch~ A that can be
used to solve a general class of constrained k-rank approximation problems to within (1+ ε) …

Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR
Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It …

We consider low-rank reconstruction of a matrix using a subset of its columns and present
asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction …

The CUR decomposition of an m× n matrix A finds an m× c matrix C with a small subset of c<
n columns of A, together with an r× n matrix R with a small subset of r< m rows of A, as well …

Randomized Numerical Linear Algebra (RandNLA) is an area which uses randomness,
most notably random sampling and random projection methods, to develop improved …

The CUR matrix decomposition and the Nyström approximation are two important low-rank
matrix approximation techniques. The Nyström method approximates a symmetric positive …

The randomly pivoted Cholesky algorithm (RPCholesky) computes a factorized rank‐kk
approximation of an N× NN*N positive‐semidefinite (psd) matrix. RPCholesky requires only …