Fig. 1

Rows 2–4 and 7–9 reconstruction of a piecewise polynomial function of degree two shown in the top row over 256 (top 5 plots) and 1024 (bottom 5 plots) points from random sampling at 50%. The corresponding least squares solution is shown in the fifth plot, and the third-order finite difference of the HOTV3 solution over the 1024 grid is shown on the bottom