Some points on the unit disk.

In this homepage we list some sets of points on the unit disk. Each set is stored in a Matlab file, that is actually a Matlab function. Its input is a degree (that varies from set to set).

The typical output of these routines are The variable stats_matrix is a matrix whose columns are

New sets

Our purpose is to achieve better results either in terms of Lebesgue constant either of Vandermonde determinants for unisolvent sets on the unit disk. For the complete description see the paper:
M. Briani, A. Sommariva, M. Vianello: "Computing Fekete and Lebesgue points: simplex, square, disk".

The results are listed below. The set LEB has particularly low Lebesgue constant, while the set FEK has particularly high absolute values of Vandermonde determinants (w.r.t. Koornwinder II basis).
1 1.66666e+00 1.66666e+00
2 1.98882e+00 1.98889e+00
3 2.46712e+00 2.63051e+00
4 2.97321e+00 3.19006e+00
5 3.50396e+00 3.85218e+00
6 4.30163e+00 4.38492e+00
7 5.08102e+00 5.58331e+00
8 5.42679e+00 6.44660e+00
9 6.72990e+00 7.02124e+00
10 8.48685e+00 7.84479e+00
11 1.03165e+01 8.91868e+00
12 1.14822e+01 1.48496e+01
13 1.19771e+01 1.70223e+01
14 1.23882e+01 1.85145e+01
15 1.41646e+01 2.14413e+01
16 1.74375e+01 2.89097e+01
1 4.94884e-01 4.94884e-01
2 2.12581e+00 2.12596e+00
3 2.97745e+01 3.43700e+01
4 2.07842e+03 3.48899e+03
5 7.03580e+05 2.03386e+06
6 1.10256e+10 1.12671e+10
7 4.15306e+13 4.20169e+14
8 2.87535e+19 1.81089e+20
9 1.74423e+25 1.02462e+27
10 2.28398e+34 6.71855e+34
11 2.96657e+38 4.88383e+43
12 1.06066e+48 6.50595e+53
13 4.08248e+58 7.10538e+64
14 2.34232e+76 3.03916e+77
15 2.38002e+89 1.57432e+91
16 3.51709e+97 6.73852e+105
1 2.98787e+00 2.98787e+00
2 5.13352e+00 5.33265e+00
3 1.08730e+01 1.06179e+01
4 1.32763e+01 1.38758e+01
5 1.55726e+01 1.64950e+01
6 2.84505e+01 2.64576e+01
7 2.55160e+01 3.28434e+01
8 3.58843e+01 4.32800e+01
9 5.34490e+01 4.79974e+01
10 6.37297e+01 6.08951e+01
11 7.85848e+01 6.88040e+01
12 1.06035e+02 7.40490e+01
13 9.55036e+01 1.09216e+02
14 1.18076e+02 1.11901e+02
15 1.52596e+02 1.25213e+02
16 1.43086e+02 2.31940e+02

» Matlab downloads

The set is stored in a Matlab file that can be downloaded by clicking on [m].

The Matlab codes are stored in a compressed file that can be downloaded by clicking on [zip].