820 problems

Let $u^n$ be the numerical solution produced by the nonuniform-time-step GBDF2-IMEX scheme … Here $\tau=\max_{0\leq k\leq M-1}\{\Delta t_k\}$ is the maximum time step, and $h_x$ an…

Let $N(d,t)$ denote the smallest cardinality of a spherical $t$-design on the $(d-1)$-dimensional sphere, and let $C_d$ be a sufficiently large positive constant depending only on…

Kung–Traub conjecture. The order satisfies

Let the linear multistep neural network loss have infinitely many global minimizers because the governing-function components $f_n$ are underdetermined by the training equations, a…

Well-definedness conjecture. The experimental conductivity $\gamma_{\mathrm{exp}}$ is well defined for every conductivity $\gamma\in\mathcal{G}^R$.

de Boor's conjecture. The interpolation by polynomial B-splines of degree $d$ at node averages is bounded by a function depending only on $d$, regardless of the nodes themselves.

Let $p$ denote the polynomial degree of a discontinuous Galerkin (DG) spatial discretization, and consider its dispersion-dissipation relations for a linear hyperbolic problem. Hu–…

Exponential-growth conjecture. The function $M$ grows exponentially as $x\to\infty$. This model arises from numerical analytic continuation and asks how rapidly a band-limited func…

Let the points $x_1,dots,x_N$ be iid drawn from a bounded probability density function $\rho$ with support in $D=[0,1]^d$. Let the Matérn kernel with parameters $\nu$ and $\ell$ be…

Let $\mathcal M$ be the parameter set, let $H$ be the coarse-mesh size, let $ell$ be the oversampling parameter, and let … be the localization error indicator for $mu\in\mathcal M$…

Let $k$ be the order of a stabilization-free serendipity virtual element method for plane elasticity, let $NE$ be the number of vertices of a regular polygonal element, and let…

Consider the proposed quadrature method applied to the nonlocal problem on a non-uniform discretization, and measure the numerical error in the $L^2$ norm. Convergence-rate conject…

Optimal uniform-rate conjecture. At least for the linear case, the optimal uniform-in-$h$ convergence rate should be $\Delta t^2$.

Let $\Omega$ be a convex and bounded domain in $\mathbb{R}^d$ with smooth boundary, and let $f^{+},f^{-}:\Omega\rightarrow\mathbb{R}_{\geq 0}$ satisfy … For a positive initial datu…

Negativity conjecture. We conjecture that

Dispersion-error blending conjecture. The blendings

Conjectured improved rate. The rate in the preceding estimate should be improvable to

The experiments concern the semi-smooth Newton method applied to positively constrained convex quadratic programming problems whose matrix $Q\in\mathbb R^{n\times n}$ does not sati…

Piecewise separable-variables approximation conjecture. It is possible to approximate $\sigma$ by a function of this form, and use it to construct a finite set of formal powers of…

Let $P$ be a finite-rank linear projector on $4\mathbb{C}[\bm{x}]4$. An ideal projector is a linear idempotent operator whose kernel is an ideal; a Lagrange projector is an ideal p…

An asynchronous variational integrator (AVI) has a multisymplectic structure expressed by the multisymplectic form formula … Here $\theta^-$ and $\theta^+$ are the boundary one-for…

RAPM two-parameter convergence conjecture. As either $C\to0^+$ or $R\to0^+$,

Let $f$ be a random complex polynomial of degree $d$, and let $c_1$ be the constant in the Renormalized Graeffe Iteration approximation theorem, under which $b\geq 1+\log_2 d$ and…

Let $F((X_t)_{t\in[0,T]})$ be a functional depending on the whole trajectory of a diffusion, and suppose its Euler approximation has a sharp weak-convergence rate of order $c/n$ or…

The paper considers path-dependent functionals of a diffusion, including lookback and barrier options, whose expectations are approximated using an Euler scheme. Their weak discret…