John Thomas Holodnak

Works (3)

Updated: July 5th, 2023 15:40

2018 journal article

A PROBABILISTIC SUBSPACE BOUND WITH APPLICATION TO ACTIVE SUBSPACES

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 39(3), 1208–1220.

By: J. Holodnak*, I. Ipsen n  & R. Smith n 

Contributors: J. Holodnak*, I. Ipsen  n & R. Smith n 

author keywords: positive semidefinite matrices; principal angles; eigenvalue decomposition; eigen-value gaps; matrix concentration inequality; intrinsic dimension; Monte Carlo sampling; active sub-spaces
TL;DR: This work presents a bound on the number of samples so that with high probability the angle between the dominant subspaces of E and S is less than a user-specified tolerance, and suggests that Monte Carlo sampling can be efficient in the presence of many parameters, as long as the underlying function f is sufficiently smooth. (via Semantic Scholar)
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Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 7, 2019

2015 journal article

CONDITIONING OF LEVERAGE SCORES AND COMPUTATION BY QR DECOMPOSITION

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 36(3), 1143–1163.

By: J. Holodnak n, I. Ipsen n  & T. Wentworth*

Contributors: J. Holodnak n, I. Ipsen  n & T. Wentworth*

author keywords: principal angles; stable rank; condition number; row-scaling; componentwise perturbations
TL;DR: The leverage scores of a full-column rank matrix A are the squared row norms of any orthonormal basis for range(A) and it is shown that corresponding leverage Scores of two matrices A and A + \Delta A are close in the relative sense, if they have large magnitude and if all principal angles between the column spaces of A & A are small. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 journal article

RANDOMIZED APPROXIMATION OF THE GRAM MATRIX: EXACT COMPUTATION AND PROBABILISTIC BOUNDS

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 36(1), 110–137.

By: J. Holodnak n & I. Ipsen n 

Contributors: J. Holodnak n & I. Ipsen  n

author keywords: leverage scores; singular value decomposition; stable rank; coherence; matrix concentration inequalities; unbiased estimator
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

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