New bounds on perturbations of extremal singular values and condition numbers under random noise via regional stability and contour analysis, with stronger results for the smallest singular value when the matrix dominates the noise.
Higham,Accuracy and stability of numerical algorithms, SIAM, 2002
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Eigenvalue stability and new perturbation bounds for the extremal eigenvalues of a matrix
New bounds on perturbations of extremal singular values and condition numbers under random noise via regional stability and contour analysis, with stronger results for the smallest singular value when the matrix dominates the noise.