7 problems

Wilkinson quadratic convergence conjecture. There exists a subset $\mathcal{X}\subset \mathcal{T}_\Lambda$ of Hausdorff codimension $1$ consisting of unreduced matrices $T$ such th…

Quadratic convergence locus conjecture. There exists a subset $\mathcal{X}\subset {\cal T}_\Lambda$ of Hausdorff codimension $1$ consisting of initial conditions $T$ for which the…

Spectral convergence conjecture. The difference in convergence rates between the Lanczos approach applied to the Hermitian TDA Hamiltonian and to $H^{\text{no coupl}}$ is due to di…

Quadratic convergence-to-singular-support conjecture. For a strong a.p. diagonal $ntimes n$ matrix $ambda$, there exists a set $\mathcal{X}subsetmathcal{T}_{ambda}$ of Hausdorff co…

Quadratic convergence conjecture. If $ambda$ is strong a.p., then there exists $\mathcal{X}subsetmathcal{T}_ambda$ of Hausdorff codimension $1$ such that the rate of convergence fo…

Consider the divide-and-conquer algorithm described immediately before the claim for the eigenvalue problem and singular value decomposition, which uses QR factorization and matrix…

Let $H$ be a dense upper Hessenberg matrix, let $m$ denote the number of QR-iteration passes combined into one, and let $M$ be the fast-memory size. The cited improvements combine…