Phuc Tran

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math.NA2026

Eigenvalue stability and new perturbation bounds for the extremal eigenvalues of a matrix

Phuc Tran, Van Vu

Let $A$ be a full ranked $n \times n$ matrix, with singular values $I ¨ _{1} (A) \geq \dots \geq I ¨ _{n} (A) > 0$ . The condition number $I^º (A) := I ¨ _{1} (A) / I ¨ _{n} (A) = ∥ A ∥ \cdot ∥ A ∥^{- 1}$ is a k…

math.NA2026

Matrices perturbed by random noise: The accuracy of low-rank approximation

Phuc Tran, Van Vu

Let $A$ be an $m \times n$ matrix with rank $r$ and singular value decomposition $A = \sum_{i = 1}^{r} σ_{i} u_{i} v_{i}^{⊤},$ where the $σ_{i}$ are its singular values, ordered decreasingl…