4 problems

Let $A$ be a nonsingular matrix and let $u$ and $v$ be vectors such that $A+uv^T$ is nonsingular. Let $\epsilon_M$ denote the unit roundoff, and let…

Let $A$ be a matrix, let $u$ and $v$ be vectors, and let $\tilde A=A+uv^T$. Let $\epsilon_M$ denote the unit roundoff, and let $\kappa_2(\cdot)$ denote the matrix 2-norm condition…

Quadratic conditioning conjecture. The conditioning of the problem scales with the mesh size $h$ squared; in particular, each mesh refinement step reduces the size of the smallest…

Let ${\cal P}$ be a set of distributions on ${\cal X}\times{\cal Y}$, and let $\delta_{\mathrm{prior}}$ denote the a priori minimax-optimal decision rule. A partition…