ABSTRACT
Figure 8.2 gives the interpolants and their error when using the minimum energy and eigenvalue points for n = 19, corresponding to m = dn =■ 400. For the minimum energy points we have ||An/ — /||oo 0.3, while for the eigenvalue points ||An/ — /||oo 0.07. This difference in the error is reflected in the different scales on the error plots. More striking still is the globally different nature of the two approximations: the interpolant with the eigenvalue points is qualitatively the true cosine cap, whereas the interpolant with the minimum energy points completely fails to reflect the locally supported nature of the cosine cap function.
