71 citations · 76 across the 5 of their papers we have counts for
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A Probabilistic Subspace Bound with Application to Active Subspaces
John T. Holodnak, Ilse C. F. Ipsen, Ralph C. Smith
Given a real symmetric positive semi-definite matrix E, and an approximation S that is a sum of n independent matrix-valued random variables, we present bounds on the relative erro…
Conditioning of Leverage Scores and Computation by QR Decomposition
John T. Holodnak, Ilse C. F. Ipsen, Thomas A. Wentworth
The leverage scores of a full-column rank matrix A are the squared row norms of any orthonormal basis for range(A). We show that corresponding leverage scores of two matrices A and…
Randomized Approximation of the Gram Matrix: Exact Computation and Probabilistic Bounds
John T. Holodnak, Ilse C. F. Ipsen
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for…