5 problems

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.

Fix $k$, and consider the Hermite interpolation error for splines of degree $2k-1$ on knot configurations $0=\tau_0<\tau_1<\cdots<\tau_{2k-4}<\tau_{2k-3}=1$. For equally spaced kno…

Let $k$ be the spline parameter, let $f$ be a $(k-1)$-times differentiable function whose $(k-1)$st derivative has finite total variation, and let $\mathcal{E}_k(f)$ denote the int…

Let $\bm{x}$ be a set of unisolvent interpolation points, let $c(\bm{x})$ denote the equioscillating spline associated with these points, let $I(1)$ denote the integral of the cons…

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