Meghaichi and Xing (arXiv:2606.12632) discretise nonlinear conservation laws with uncertainty by replacing the multiplication on the space P_K of polynomials of degree at most K in the random variable by an associative truncated product (ATP), and they tabu…
Let Tm(m)(B) = I + B + … + Bᵐ⁻¹ be the radix-m kernel of the truncated Neumann series and let μₘ be the least number of matrix products with which a straight-line program (products of linear combinations, starting from I and B; additions and scalings free)…
Let πₙᶜⁱʳᶜ be the real polynomials of degree at most n bounded by 1 on [-1,1] and Tₙ the Chebyshev polynomial. Bojanov's problem, as recorded by Naidenov, asks whether ∫₋₁¹φ(|P^((k))|)<∫₋₁¹φ(|Tₙ^((k))|) for every strictly increasing convex φ, every P ∈ πₙᶜⁱ…
Chen, Edelman and Urschel have recently attached to the maximal growth factor of Gaussian elimination with complete pivoting on 5 × 5 matrices an explicit integer polynomial P₅ of degree 61, conjecturing that the growth factor is its unique real root in [4,…
Cui, Ding and Wu introduced the optimal cell average decomposition (OCAD) problem, whose solution is exactly the largest bound-preserving CFL number of a Zhang–Shu limited high-order scheme on a Cartesian cell. They solved it for the tensor-product spaces ℚ…
