Randomized algorithms in numerical linear algebra 1

Mark Tygert
Yale University

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.

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