10 problems

Condition-number monotonicity conjecture. For the Gaussian or inverse multiquadric RBF,

Let $n$ be an odd dimension, let $d\in\mathbb{N}$, and let $Q_h$ be the quasi-interpolant constructed from the generalized multiquadric function…

Let $z_j\geqslant0$ be independent random variables satisfying the sixth moment condition and the mean condition, and write $z_{1:d}=(z_1,\ldots,z_d)$. For a function $f$, let…

The RBF approximation uses a shape parameter, denoted by $\epsilon$, and consistency means that the truncation error tends to zero as the step size $h\to 0$. The approximation has…

Saturation-order conjecture. The uniform norm of the error decays with saturation order

Generalized native-space inclusion conjecture. The native space $\mathcal{N}_G^{\mathscr{P}}(\mathbb{R}^2)$ associated with $G$ and $\mathscr{P}$ is a subspace of…

Let $\tau$, $t$, $\tau$, $h_{X,\Gamma}$, $k$, and $r$ be the parameters and mesh-related quantities defined for the radial basis function discretization, and let $\phi$ and…

Let $\Xi$ be a quasiuniform subset of $SO(3)$ with mesh ratio $\rho$. For the kernel $k_m$ on $SO(3)$ and its associated space $S(k_m,\Xi)$, let $\chi_{\xi}$ denote the Lagrange fu…

Let $\Xi$ be a quasiuniform center set with mesh ratio $\rho$, and let $\phi_{\beta}=G_{\beta}+G_{\beta}*\psi$ with $\beta>d$. Let $S(\phi_{\beta},\Xi)$ be the associated kernel sp…

Let $\Xi$ be a quasiuniform set of centers on the sphere, with mesh ratio $\rho$. For restricted surface splines $\varphi_m$ and the associated conditionally positive-definite kern…