8 problems

Longer-chain improvement conjecture. Running these chains longer is likely to result in improved estimation.

Nesting-convergence conjecture. The nesting technique helps the parametric models to focus on the most important signals, and thus improves the overall convergence.

Let $\bm{u}_1,\ldots,\bm{u}_r$ and $\bm{v}_1,\ldots,\bm{v}_r$ be the signal's left and right singular vectors, and let $\hat{\bm{u}}_1,\ldots,\hat{\bm{u}}_r$ and…

Let $\mathbb{DC}$ denote the dual complex numbers and $\mathbb{DR}$ the dual real numbers, with $\epsilon^2=0$. A rank-$k$ dual complex matrix $\bm{A}_k$ is a dual complex matrix w…

Similarity characterization conjecture. The Jordan SVD exists if and only if $AB$ is similar to $BA$.

Failure of the minimal subspace property conjecture. There exist functions $u\in H^1(\Omega)$ that do not satisfy the statement of Theorem $$ .

The randomized spectral divide-and-conquer algorithms apply to eigenvalue problems for regular pencils, nonsymmetric and symmetric eigenvalue problems for a single matrix, and the…

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…