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math.NA2025
Davis-Kahan Theorem under a moderate gap condition
Phuc Tran, Van Vu
The classical Davis-Kahan theorem provides an efficient bound on the perturbation of eigenspaces of a matrix under a large (eigenvalue) gap condition. In this paper, we consider th…
math.NA2024
Matrix perturbation bounds via contour bootstrapping
Phuc Tran, Van Vu
Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new…