… Subsequently, Drineas and Zouzias18 introduced the idea of using matrix measure
concentration inequalities37,40,47 to simplify the proofs, and follow-up work18 has improved …

… of Drineas, Kannan, and Mahoney (2004a,b,c) that will be useful for the proofs in this paper;
see also Drineas, … randomized SVD and CUR algorithms (Drineas, Kannan, and Mahoney, …

… Inequality (6) follows since CC + is a projection matrix and thus does not increase the
Frobenius norm, and the last equality follows since P C = CC + and similarly P R = R + R. Since A…

… Using the sampling matrix formalism described previously (Drineas et al., 2006a,b, 2008, …
a combination of Lemmas 3 and 4 from Drineas et al. (2010b), restated to fit our notation). …

… Our goal is to find an approximation P to A, such that the rank of P is at most k, satisfying (…
P is almost the best rank k approximation to A in the sense described above. The matrix P …

… c randomly chosen columns of A (suitably rescaled) and R ∈ Rc×p is a matrix whose
rows are the c corresponding rows of B (also suitably rescaled). An important aspect of this …

Motivated by applications in which the data may be formulated as a matrix, we consider
algorithms for several common linear algebra problems. These algorithms make more efficient …

… Let DST A be the r × n matrix consisting of the sampled and appropriately rescaled rows
of the original matrix A, and let DST B be the r × p matrix consisting of the sampled and …

Least squares approximation is a technique to find an approximate solution to a system of
linear equations that has no exact solution. In a typical setting, one lets n be the number of …

… the spectral norm, the best previouslyknown bound for approximating the CSSP is p(k, n) =
… Maggioni, and P. Drineas. TensorCUR decompositions for tensor-based data. SIAM J Matrix …