5 problems

Let $\widetilde{A}$ be an $n\times n$ matrix with $\|\widetilde{A}\|_2\leq 1$, and let $A$ be a Gaussian perturbation of $\widetilde{A}$ with variance $\sigma^2\leq1$. Let $U$ be t…

Let $A=B+iC\in\mathcal A_n$, where $B$ and $C$ are the real and imaginary parts of an accretive-dissipative matrix, and suppose that … Here $\kappa$ denotes the condition number an…

Superlinear growth conjecture. The maximum growth factor is superlinear:

For each positive integer $n$, let $g\big[\mathbf{CP}_n(\mathbb{R})\big]$ be the maximum growth factor for complete pivoting over real $n\times n$ matrices. Complete-pivoting thres…

Let $g\big[\mathbf{CP}_n(\mathbb{R})\big]$ denote the maximum growth factor for complete pivoting over real $n\times n$ matrices. Wilkinson's conjecture. … with equality achieved o…