6 problems

Matrix inverse realization conjecture. Each entry of $\mathfrak A^{-1}$ is a noncommutative rational expression in the entries of $\mathfrak A$: there exist noncommutative rational…

Let ${\bf A}$ be an invertible matrix and consider stochastic quasi-Newton rules obtained by applying the paper's stochastic reformulation and its basic, parallel, or accelerated s…

The Hsu–Ma $(\alpha,\beta)$-inversion formula. The matrices $F=(F(n,k))_{n\geq k\in\mathbb{Z}}$ and $G=(G(n,k))_{n\geq k\in\mathbb{Z}}$ are inverse matrices if and only if, for arb…

Let $A\in\mathbb{R}^{n\times n}$ be a nonsingular matrix whose inverse has only nonzero elements in the lower triangle. Let $X$ be the inverse computed numerically by algorithm (KW…

Let $A\in\mathbb{R}^{n\times n}$ be a tridiagonal matrix, and let $X$ be its inverse computed using the proposed algorithm. Let $\varepsilon$ denote the machine precision, let…

Auriac–Maillard–Viallet conjecture. For every $q\geq 3$,