5 problems

The nearly quadratic-time conjecture for arbitrary-vector kernel matrix-vector products
arXiv@arxiv
Kernel matrices may be applied to arbitrary vectors, including vectors with both positive and negative coordinates. Nearly quadratic-time conjecture. The arbitrary-vector case may…
Conjectureopenfine-grained-complexity kernel-matrices matrix-vector-products
1
Frequency-localisation conjecture for eigenvectors of completely smooth kernels
arXiv@arxiv
Consider eigenvectors of kernel matrices arising from completely smooth kernels and, for comparison, finitely smooth kernels; at low energies, distinguish localisation in frequency…
Conjecturerefutedkernel-matrices spectral-localisation
0
Conjecture on limiting eigenvectors of smooth kernel matrices
arXiv@arxiv
Limiting-eigenvector conjecture. The limiting eigenvectors in the $\mathcal{O}(\varepsilon^{2s})$ group are the columns of $\boldsymbol{Q}_{s}\boldsymbol{U}_{s}$ , where…
Conjecturerefutedasymptotic-analysis kernel-matrices spectral-theory
0
Bounded spectral norm of random kernel matrices
arXiv@arxiv
Bounded spectral norm conjecture. For random kernel matrices, $s(A_l)$ is conjectured to be $\mathcal{O}(1)$ .
Conjectureopenkernel-matrices random-matrices spectral-theory
0
Bounded spectral extremes of random inner-product kernel matrices
arXiv@arxiv
Bounded spectral extremes conjecture. Numerical simulations suggest that the largest and smallest eigenvalues lie at the right and left ends, respectively, of the support of the li…
Conjectureopenkernel-matrices random-matrices spectral-theory
0

5 problems

The nearly quadratic-time conjecture for arbitrary-vector kernel matrix-vector products

Frequency-localisation conjecture for eigenvectors of completely smooth kernels

Conjecture on limiting eigenvectors of smooth kernel matrices

Bounded spectral norm of random kernel matrices

Bounded spectral extremes of random inner-product kernel matrices