We will survey randomized algorithms for solving three problems in
numerical linear algebra:
(1) the estimation of the spectral norms of matrices,
(2) linear least-squares regression (solving overdetermined systems
of linear-algebraic equations in the least-squares sense), and
(3) the low-rank approximation of matrices (which is more or less
equivalent to computing several of the greatest singular values and
corresponding singular vectors).
These algorithms encompass work by many researchers.