3 problems

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 $f$ be approximated from function and gradient measurements, with the gradient sampled at points independent of the function-sampling points but drawn from the same sampling de…

Let $p\in[0,1]$ be the fraction of gradient samples taken. Consider the Hermite interpolation setting in which function values are sampled at the full set of points but gradients a…