7 problems

Let GD denote gradient descent, and let the solution manifold be the set of global minimisers of the overparametrised least-squares problem. A tubular neighbourhood is a neighbourh…

Convergence of SVS-SPRING for LLQ. Under these assumptions and the SVS$(J,k,\lambda)$ sampling distribution, SPRING should satisfy the displayed convergence bound, where the hidden…

Let $\boldsymbol{A}\in\mathbb{R}^{m\times n}$ be the least-squares matrix, and let $\boldsymbol{R}$ be computed from $\boldsymbol{A}$ by sketching and $\textsf{QR}$ factorizing the…

Two-step convergence conjecture. The method has two steps: discovery of the active set and Krylov convergence.

Let $\widehat{\lambda}_{\mathrm{min}}^+$ denote the smallest positive eigenvalue of the relevant empirical covariance or Gram matrix, and let the double descent phenomenon mean the…

Let a block Kaczmarz method update an iterate using a block containing many rows of the system matrix, and let a projection update enforce consistency with the corresponding null-s…

Non-negative least-squares column-exclusion conjecture. There exists at least one column ${\bf g}_*$ of $G$ such that $\hat{\bf x}$ has non-negative entries.