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math.SP2024
New matrix perturbation bounds with relative strength: Perturbation of eigenspaces
Phuc Tran, Van Vu
Matrix perturbation bounds (such as Weyl and Davis--Kahan) are used abundantly in many areas of mathematics and data science. Many bounds (such as the above two) involve the spectr…
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…