Sets on the unit-disk
The purpose of this homepage is to gather interpolation sets on the unit disk, determining their properties, such as Lebesgue constant, absolute value of the Vandermonde determinant w.r.t. a certain Koornwinder basis as well as its conditioning. For software about AFP and DLP see [.zip]. All the files have been determined by G. Meurant and A. Sommariva.
AFP (Approximate Fekete Points)
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.164e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
5.295e+00 |
0 |
3 |
10 |
2.631e+00 |
4.862e+03 |
1.589e+01 |
0 |
4 |
15 |
3.190e+00 |
6.731e+06 |
2.433e+01 |
0 |
5 |
21 |
3.853e+00 |
9.043e+10 |
3.438e+01 |
0 |
6 |
28 |
4.385e+00 |
1.943e+16 |
3.971e+01 |
0 |
7 |
36 |
5.585e+00 |
4.713e+22 |
5.990e+01 |
0 |
8 |
45 |
6.449e+00 |
2.213e+30 |
6.968e+01 |
0 |
9 |
55 |
7.022e+00 |
2.280e+39 |
9.173e+01 |
0 |
10 |
66 |
7.847e+00 |
4.543e+49 |
1.035e+02 |
0 |
11 |
78 |
8.920e+00 |
1.673e+61 |
1.353e+02 |
0 |
12 |
91 |
1.485e+01 |
1.882e+74 |
1.515e+02 |
0 |
13 |
105 |
1.702e+01 |
2.887e+88 |
2.160e+02 |
0 |
14 |
120 |
1.851e+01 |
2.886e+104 |
2.100e+02 |
0 |
15 |
136 |
2.145e+01 |
5.808e+121 |
1.931e+02 |
0 |
16 |
153 |
2.892e+01 |
1.605e+140 |
2.756e+02 |
0 |
17 |
171 |
3.040e+01 |
8.218e+160 |
3.690e+02 |
0 |
18 |
190 |
3.276e+01 |
4.343e+182 |
3.923e+02 |
0 |
19 |
210 |
4.132e+01 |
1.188e+206 |
4.952e+02 |
0 |
20 |
231 |
3.219e+01 |
2.447e+231 |
5.261e+02 |
0 |
» SOURCE: L. Bos, S. De Marchi, A. Sommariva and M. Vianello, Computing multivariate Fekete and Leja points by numerical linear algebra, SIAM J. Numer. Anal., 48 (2010), pp. 1984-1999
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
DLP (Discrete Leja Points)
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
3.000e+00 |
1.437e+00 |
4.000e+00 |
0 |
2 |
6 |
5.000e+00 |
2.413e+01 |
6.197e+00 |
0 |
3 |
10 |
7.000e+00 |
2.550e+03 |
1.692e+01 |
0 |
4 |
15 |
9.000e+00 |
3.276e+06 |
2.122e+01 |
0 |
5 |
21 |
1.139e+01 |
1.167e+10 |
4.866e+01 |
0 |
6 |
28 |
1.300e+01 |
1.808e+15 |
5.855e+01 |
0 |
7 |
36 |
1.500e+01 |
1.147e+21 |
9.781e+01 |
0 |
8 |
45 |
2.052e+01 |
1.776e+28 |
1.301e+02 |
0 |
9 |
55 |
2.606e+01 |
9.142e+36 |
2.214e+02 |
0 |
10 |
66 |
2.437e+01 |
8.583e+46 |
1.751e+02 |
0 |
11 |
78 |
5.678e+01 |
3.348e+57 |
3.584e+02 |
0 |
12 |
91 |
4.487e+01 |
7.667e+69 |
2.834e+02 |
0 |
13 |
105 |
9.061e+01 |
6.073e+82 |
1.035e+03 |
0 |
14 |
120 |
9.232e+01 |
1.381e+98 |
1.090e+03 |
0 |
15 |
136 |
6.133e+01 |
3.697e+114 |
5.852e+02 |
0 |
16 |
153 |
5.995e+01 |
1.799e+133 |
5.959e+02 |
0 |
17 |
171 |
9.907e+01 |
1.048e+152 |
1.860e+03 |
0 |
18 |
190 |
9.498e+01 |
2.364e+174 |
1.491e+03 |
0 |
19 |
210 |
1.538e+02 |
3.384e+196 |
1.907e+03 |
0 |
20 |
231 |
1.969e+02 |
6.976e+219 |
4.246e+03 |
0 |
» SOURCE: L. Bos, S. De Marchi, A. Sommariva and M. Vianello, Computing multivariate Fekete and Leja points by numerical linear algebra, SIAM J. Numer. Anal., 48 (2010), pp. 1984-1999
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
Carnicer-Godes
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
2.624e+00 |
4.825e+03 |
1.721e+01 |
0 |
4 |
15 |
3.234e+00 |
6.733e+06 |
2.450e+01 |
0 |
5 |
21 |
3.721e+00 |
9.153e+10 |
3.180e+01 |
0 |
6 |
28 |
4.324e+00 |
1.621e+16 |
5.006e+01 |
0 |
7 |
36 |
4.983e+00 |
3.217e+22 |
5.893e+01 |
0 |
8 |
45 |
5.555e+00 |
1.262e+30 |
8.059e+01 |
0 |
9 |
55 |
6.182e+00 |
7.598e+38 |
9.148e+01 |
0 |
10 |
66 |
6.749e+00 |
1.361e+49 |
1.113e+02 |
0 |
11 |
78 |
7.406e+00 |
2.108e+60 |
1.354e+02 |
0 |
12 |
91 |
8.163e+00 |
1.196e+73 |
1.451e+02 |
0 |
13 |
105 |
8.991e+00 |
1.466e+87 |
1.833e+02 |
0 |
14 |
120 |
1.005e+01 |
4.278e+102 |
2.124e+02 |
0 |
15 |
136 |
1.122e+01 |
2.963e+119 |
2.387e+02 |
0 |
16 |
153 |
1.249e+01 |
5.964e+137 |
2.378e+02 |
0 |
17 |
171 |
1.421e+01 |
2.753e+157 |
2.975e+02 |
0 |
18 |
190 |
1.600e+01 |
4.265e+178 |
3.211e+02 |
0 |
19 |
210 |
1.815e+01 |
1.708e+201 |
2.889e+02 |
0 |
20 |
231 |
2.082e+01 |
2.014e+225 |
5.217e+02 |
0 |
21 |
253 |
2.388e+01 |
7.503e+250 |
4.540e+02 |
0 |
22 |
276 |
2.731e+01 |
1.001e+278 |
5.901e+02 |
0 |
23 |
300 |
3.186e+01 |
3.227e+306 |
6.236e+02 |
0 |
24 |
325 |
3.690e+01 |
Inf |
8.785e+02 |
0 |
25 |
351 |
4.283e+01 |
Inf |
9.040e+02 |
0 |
26 |
378 |
5.020e+01 |
Inf |
1.282e+03 |
0 |
27 |
406 |
5.901e+01 |
Inf |
1.358e+03 |
0 |
28 |
435 |
6.911e+01 |
Inf |
2.130e+03 |
0 |
29 |
465 |
8.157e+01 |
Inf |
2.412e+03 |
0 |
30 |
496 |
9.696e+01 |
Inf |
2.405e+03 |
0 |
31 |
528 |
1.141e+02 |
Inf |
4.344e+03 |
0 |
32 |
561 |
1.349e+02 |
Inf |
4.528e+03 |
0 |
33 |
595 |
1.615e+02 |
Inf |
6.554e+03 |
0 |
34 |
630 |
1.915e+02 |
Inf |
5.393e+03 |
0 |
35 |
666 |
2.275e+02 |
Inf |
9.606e+03 |
0 |
36 |
703 |
2.727e+02 |
Inf |
1.053e+04 |
0 |
37 |
741 |
3.283e+02 |
Inf |
9.916e+03 |
0 |
38 |
780 |
3.926e+02 |
Inf |
8.837e+03 |
0 |
39 |
820 |
4.682e+02 |
Inf |
1.088e+04 |
0 |
40 |
861 |
5.585e+02 |
Inf |
2.359e+04 |
0 |
41 |
903 |
6.791e+02 |
Inf |
2.848e+04 |
0 |
42 |
946 |
8.179e+02 |
Inf |
2.721e+04 |
0 |
43 |
990 |
9.811e+02 |
Inf |
5.077e+04 |
0 |
44 |
1035 |
1.173e+03 |
Inf |
4.139e+04 |
0 |
45 |
1081 |
1.401e+03 |
Inf |
7.527e+04 |
0 |
46 |
1128 |
1.682e+03 |
Inf |
4.567e+04 |
0 |
47 |
1176 |
2.043e+03 |
Inf |
1.131e+05 |
0 |
48 |
1225 |
2.478e+03 |
Inf |
6.670e+04 |
0 |
49 |
1275 |
3.010e+03 |
Inf |
1.457e+05 |
0 |
50 |
1326 |
3.661e+03 |
Inf |
1.022e+05 |
0 |
» SOURCE: J.M. Carnicer and C. Godes, Interpolation on the disk, Numer. Algo., 66 (2014), pp. 1-16
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=0
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
2.629e+00 |
4.723e+03 |
1.448e+01 |
0 |
4 |
15 |
3.254e+00 |
6.786e+06 |
2.430e+01 |
0 |
5 |
21 |
3.762e+00 |
9.009e+10 |
3.188e+01 |
0 |
6 |
28 |
4.763e+00 |
1.856e+16 |
4.887e+01 |
0 |
7 |
36 |
5.613e+00 |
4.561e+22 |
5.756e+01 |
0 |
8 |
45 |
6.278e+00 |
2.160e+30 |
8.240e+01 |
0 |
9 |
55 |
7.703e+00 |
1.473e+39 |
7.962e+01 |
0 |
10 |
66 |
9.065e+00 |
2.280e+49 |
8.872e+01 |
0 |
11 |
78 |
1.053e+01 |
5.869e+60 |
1.229e+02 |
0 |
12 |
91 |
1.263e+01 |
3.903e+73 |
1.651e+02 |
0 |
13 |
105 |
1.548e+01 |
4.844e+87 |
2.172e+02 |
0 |
14 |
120 |
1.865e+01 |
1.723e+103 |
2.162e+02 |
0 |
15 |
136 |
2.246e+01 |
1.257e+120 |
3.972e+02 |
0 |
16 |
153 |
2.844e+01 |
2.863e+138 |
5.450e+02 |
0 |
17 |
171 |
3.570e+01 |
1.445e+158 |
4.849e+02 |
0 |
18 |
190 |
4.448e+01 |
2.445e+179 |
1.025e+03 |
0 |
19 |
210 |
5.650e+01 |
9.789e+201 |
1.417e+03 |
0 |
20 |
231 |
7.288e+01 |
1.394e+226 |
1.291e+03 |
0 |
21 |
253 |
9.344e+01 |
4.960e+251 |
1.789e+03 |
0 |
22 |
276 |
1.197e+02 |
6.602e+278 |
2.600e+03 |
0 |
23 |
300 |
1.569e+02 |
2.300e+307 |
5.268e+03 |
0 |
24 |
325 |
2.051e+02 |
Inf |
7.342e+03 |
0 |
25 |
351 |
2.675e+02 |
Inf |
1.017e+04 |
0 |
26 |
378 |
3.514e+02 |
Inf |
1.416e+04 |
0 |
27 |
406 |
4.638e+02 |
Inf |
1.957e+04 |
0 |
28 |
435 |
6.118e+02 |
Inf |
2.721e+04 |
0 |
29 |
465 |
8.082e+02 |
Inf |
3.754e+04 |
0 |
30 |
496 |
1.073e+03 |
Inf |
5.218e+04 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=0.5
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
2.659e+00 |
4.448e+03 |
1.775e+01 |
0 |
4 |
15 |
3.341e+00 |
6.226e+06 |
2.469e+01 |
0 |
5 |
21 |
3.893e+00 |
8.110e+10 |
3.513e+01 |
0 |
6 |
28 |
4.381e+00 |
1.699e+16 |
4.779e+01 |
0 |
7 |
36 |
5.161e+00 |
4.352e+22 |
4.845e+01 |
0 |
8 |
45 |
5.756e+00 |
2.233e+30 |
6.310e+01 |
0 |
9 |
55 |
6.718e+00 |
1.701e+39 |
9.619e+01 |
0 |
10 |
66 |
7.775e+00 |
3.064e+49 |
1.082e+02 |
0 |
11 |
78 |
8.911e+00 |
9.511e+60 |
1.252e+02 |
0 |
12 |
91 |
1.035e+01 |
7.947e+73 |
1.238e+02 |
0 |
13 |
105 |
1.242e+01 |
1.288e+88 |
1.638e+02 |
0 |
14 |
120 |
1.467e+01 |
6.238e+103 |
1.441e+02 |
0 |
15 |
136 |
1.721e+01 |
6.449e+120 |
2.679e+02 |
0 |
16 |
153 |
2.133e+01 |
2.173e+139 |
3.542e+02 |
0 |
17 |
171 |
2.618e+01 |
1.691e+159 |
4.679e+02 |
0 |
18 |
190 |
3.190e+01 |
4.606e+180 |
3.925e+02 |
0 |
19 |
210 |
3.972e+01 |
3.096e+203 |
5.726e+02 |
0 |
20 |
231 |
5.027e+01 |
7.737e+227 |
1.124e+03 |
0 |
21 |
253 |
6.329e+01 |
5.042e+253 |
1.024e+03 |
0 |
22 |
276 |
7.943e+01 |
1.285e+281 |
2.056e+03 |
0 |
23 |
300 |
1.027e+02 |
Inf |
2.801e+03 |
0 |
24 |
325 |
1.322e+02 |
Inf |
3.813e+03 |
0 |
25 |
351 |
1.697e+02 |
Inf |
5.225e+03 |
0 |
26 |
378 |
2.198e+02 |
Inf |
4.727e+03 |
0 |
27 |
406 |
2.869e+02 |
Inf |
9.803e+03 |
0 |
28 |
435 |
3.739e+02 |
Inf |
8.654e+03 |
0 |
29 |
465 |
4.877e+02 |
Inf |
1.830e+04 |
0 |
30 |
496 |
6.412e+02 |
Inf |
2.489e+04 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=1
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
2.703e+00 |
4.149e+03 |
1.817e+01 |
0 |
4 |
15 |
3.467e+00 |
5.367e+06 |
2.526e+01 |
0 |
5 |
21 |
4.151e+00 |
6.315e+10 |
3.215e+01 |
0 |
6 |
28 |
4.639e+00 |
1.199e+16 |
4.662e+01 |
0 |
7 |
36 |
5.130e+00 |
2.776e+22 |
5.902e+01 |
0 |
8 |
45 |
5.514e+00 |
1.303e+30 |
7.301e+01 |
0 |
9 |
55 |
6.133e+00 |
9.174e+38 |
8.795e+01 |
0 |
10 |
66 |
7.023e+00 |
1.555e+49 |
1.166e+02 |
0 |
11 |
78 |
7.981e+00 |
4.618e+60 |
1.193e+02 |
0 |
12 |
91 |
9.026e+00 |
3.778e+73 |
1.352e+02 |
0 |
13 |
105 |
1.065e+01 |
6.124e+87 |
1.304e+02 |
0 |
14 |
120 |
1.238e+01 |
3.047e+103 |
1.889e+02 |
0 |
15 |
136 |
1.427e+01 |
3.318e+120 |
1.744e+02 |
0 |
16 |
153 |
1.730e+01 |
1.212e+139 |
1.883e+02 |
0 |
17 |
171 |
2.084e+01 |
1.051e+159 |
3.133e+02 |
0 |
18 |
190 |
2.491e+01 |
3.293e+180 |
3.321e+02 |
0 |
19 |
210 |
3.048e+01 |
2.623e+203 |
4.265e+02 |
0 |
20 |
231 |
3.790e+01 |
8.027e+227 |
5.512e+02 |
0 |
21 |
253 |
4.687e+01 |
6.614e+253 |
9.736e+02 |
0 |
22 |
276 |
5.778e+01 |
2.205e+281 |
1.296e+03 |
0 |
23 |
300 |
7.376e+01 |
Inf |
1.747e+03 |
0 |
24 |
325 |
9.353e+01 |
Inf |
2.345e+03 |
0 |
25 |
351 |
1.183e+02 |
Inf |
3.188e+03 |
0 |
26 |
378 |
1.514e+02 |
Inf |
4.324e+03 |
0 |
27 |
406 |
1.953e+02 |
Inf |
5.900e+03 |
0 |
28 |
435 |
2.516e+02 |
Inf |
5.400e+03 |
0 |
29 |
465 |
3.239e+02 |
Inf |
1.096e+04 |
0 |
30 |
496 |
4.222e+02 |
Inf |
1.486e+04 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=1.5
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
5.481e+00 |
0 |
3 |
10 |
2.753e+00 |
3.862e+03 |
1.861e+01 |
0 |
4 |
15 |
3.616e+00 |
4.494e+06 |
2.604e+01 |
0 |
5 |
21 |
4.465e+00 |
4.555e+10 |
3.256e+01 |
0 |
6 |
28 |
5.118e+00 |
7.294e+15 |
4.718e+01 |
0 |
7 |
36 |
5.817e+00 |
1.392e+22 |
6.315e+01 |
0 |
8 |
45 |
6.393e+00 |
5.342e+29 |
8.097e+01 |
0 |
9 |
55 |
7.010e+00 |
3.044e+38 |
9.198e+01 |
0 |
10 |
66 |
7.524e+00 |
4.178e+48 |
1.175e+02 |
0 |
11 |
78 |
8.206e+00 |
1.005e+60 |
1.265e+02 |
0 |
12 |
91 |
8.788e+00 |
6.703e+72 |
1.182e+02 |
0 |
13 |
105 |
9.541e+00 |
8.920e+86 |
1.695e+02 |
0 |
14 |
120 |
1.094e+01 |
3.687e+102 |
1.851e+02 |
0 |
15 |
136 |
1.247e+01 |
3.376e+119 |
2.097e+02 |
0 |
16 |
153 |
1.480e+01 |
1.054e+138 |
1.903e+02 |
0 |
17 |
171 |
1.755e+01 |
7.938e+157 |
2.518e+02 |
0 |
18 |
190 |
2.063e+01 |
2.201e+179 |
3.447e+02 |
0 |
19 |
210 |
2.488e+01 |
1.582e+202 |
2.975e+02 |
0 |
20 |
231 |
3.042e+01 |
4.465e+226 |
5.540e+02 |
0 |
21 |
253 |
3.700e+01 |
3.469e+252 |
6.694e+02 |
0 |
22 |
276 |
4.501e+01 |
1.117e+280 |
9.369e+02 |
0 |
23 |
300 |
5.665e+01 |
Inf |
1.240e+03 |
0 |
24 |
325 |
7.082e+01 |
Inf |
1.644e+03 |
0 |
25 |
351 |
8.832e+01 |
Inf |
2.194e+03 |
0 |
26 |
378 |
1.118e+02 |
Inf |
2.073e+03 |
0 |
27 |
406 |
1.426e+02 |
Inf |
3.951e+03 |
0 |
28 |
435 |
1.815e+02 |
Inf |
5.294e+03 |
0 |
29 |
465 |
2.310e+02 |
Inf |
7.123e+03 |
0 |
30 |
496 |
2.985e+02 |
Inf |
9.535e+03 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=2
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
2.807e+00 |
3.599e+03 |
1.906e+01 |
0 |
4 |
15 |
3.780e+00 |
3.716e+06 |
2.300e+01 |
0 |
5 |
21 |
4.823e+00 |
3.156e+10 |
4.219e+01 |
0 |
6 |
28 |
5.688e+00 |
4.073e+15 |
4.825e+01 |
0 |
7 |
36 |
6.670e+00 |
6.028e+21 |
7.097e+01 |
0 |
8 |
45 |
7.526e+00 |
1.748e+29 |
8.725e+01 |
0 |
9 |
55 |
8.493e+00 |
7.340e+37 |
1.041e+02 |
0 |
10 |
66 |
9.463e+00 |
7.313e+47 |
1.079e+02 |
0 |
11 |
78 |
1.070e+01 |
1.258e+59 |
1.443e+02 |
0 |
12 |
91 |
1.176e+01 |
5.964e+71 |
1.362e+02 |
0 |
13 |
105 |
1.307e+01 |
5.604e+85 |
1.975e+02 |
0 |
14 |
120 |
1.415e+01 |
1.634e+101 |
1.730e+02 |
0 |
15 |
136 |
1.551e+01 |
1.056e+118 |
1.689e+02 |
0 |
16 |
153 |
1.659e+01 |
2.335e+136 |
2.677e+02 |
0 |
17 |
171 |
1.803e+01 |
1.253e+156 |
2.064e+02 |
0 |
18 |
190 |
1.927e+01 |
2.495e+177 |
3.107e+02 |
0 |
19 |
210 |
2.122e+01 |
1.300e+200 |
3.775e+02 |
0 |
20 |
231 |
2.555e+01 |
2.691e+224 |
3.618e+02 |
0 |
21 |
253 |
3.063e+01 |
1.553e+250 |
4.429e+02 |
0 |
22 |
276 |
3.685e+01 |
3.771e+277 |
5.083e+02 |
0 |
23 |
300 |
4.572e+01 |
2.692e+306 |
9.445e+02 |
0 |
24 |
325 |
5.639e+01 |
Inf |
8.345e+02 |
0 |
25 |
351 |
6.938e+01 |
Inf |
1.145e+03 |
0 |
26 |
378 |
8.698e+01 |
Inf |
2.091e+03 |
0 |
27 |
406 |
1.097e+02 |
Inf |
2.762e+03 |
0 |
28 |
435 |
1.381e+02 |
Inf |
3.657e+03 |
0 |
29 |
465 |
1.740e+02 |
Inf |
4.869e+03 |
0 |
30 |
496 |
2.228e+02 |
Inf |
6.462e+03 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=5
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
3.135e+00 |
2.500e+03 |
2.159e+01 |
0 |
4 |
15 |
4.910e+00 |
1.213e+06 |
3.328e+01 |
0 |
5 |
21 |
7.618e+00 |
3.060e+09 |
6.552e+01 |
0 |
6 |
28 |
1.077e+01 |
7.771e+13 |
8.726e+01 |
0 |
7 |
36 |
1.539e+01 |
1.491e+19 |
1.760e+02 |
0 |
8 |
45 |
2.094e+01 |
3.895e+25 |
2.428e+02 |
0 |
9 |
55 |
2.985e+01 |
1.035e+33 |
4.024e+02 |
0 |
10 |
66 |
3.929e+01 |
4.802e+41 |
4.348e+02 |
0 |
11 |
78 |
5.349e+01 |
2.874e+51 |
9.202e+02 |
0 |
12 |
91 |
6.857e+01 |
3.680e+62 |
1.127e+03 |
0 |
13 |
105 |
9.054e+01 |
7.362e+74 |
1.735e+03 |
0 |
14 |
120 |
1.127e+02 |
3.725e+88 |
2.112e+03 |
0 |
15 |
136 |
1.448e+02 |
3.446e+103 |
3.202e+03 |
0 |
16 |
153 |
1.774e+02 |
9.266e+119 |
3.696e+03 |
0 |
17 |
171 |
2.221e+02 |
5.190e+137 |
5.423e+03 |
0 |
18 |
190 |
2.663e+02 |
9.496e+156 |
6.177e+03 |
0 |
19 |
210 |
3.277e+02 |
4.038e+177 |
8.914e+03 |
0 |
20 |
231 |
3.889e+02 |
6.191e+199 |
7.635e+03 |
0 |
21 |
253 |
4.701e+02 |
2.421e+223 |
1.379e+04 |
0 |
22 |
276 |
5.494e+02 |
3.713e+248 |
1.505e+04 |
0 |
23 |
300 |
6.561e+02 |
1.572e+275 |
2.095e+04 |
0 |
24 |
325 |
7.588e+02 |
2.804e+303 |
2.218e+04 |
0 |
25 |
351 |
8.940e+02 |
Inf |
3.064e+04 |
0 |
26 |
378 |
1.026e+03 |
Inf |
3.230e+04 |
0 |
27 |
406 |
1.196e+03 |
Inf |
4.322e+04 |
0 |
28 |
435 |
1.362e+03 |
Inf |
4.493e+04 |
0 |
29 |
465 |
1.572e+03 |
Inf |
6.085e+04 |
0 |
30 |
496 |
1.776e+03 |
Inf |
4.296e+04 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=10
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
3.627e+00 |
1.632e+03 |
2.542e+01 |
0 |
4 |
15 |
6.966e+00 |
2.792e+05 |
5.446e+01 |
0 |
5 |
21 |
1.390e+01 |
1.145e+08 |
1.353e+02 |
0 |
6 |
28 |
2.493e+01 |
2.068e+11 |
3.071e+02 |
0 |
7 |
36 |
4.708e+01 |
1.171e+15 |
6.824e+02 |
0 |
8 |
45 |
8.016e+01 |
3.761e+19 |
1.162e+03 |
0 |
9 |
55 |
1.438e+02 |
5.067e+24 |
2.578e+03 |
0 |
10 |
66 |
2.321e+02 |
5.050e+30 |
4.253e+03 |
0 |
11 |
78 |
3.906e+02 |
2.775e+37 |
7.915e+03 |
0 |
12 |
91 |
6.042e+02 |
1.446e+45 |
1.269e+04 |
0 |
13 |
105 |
9.670e+02 |
5.307e+53 |
2.351e+04 |
0 |
14 |
120 |
1.437e+03 |
2.308e+63 |
3.297e+04 |
0 |
15 |
136 |
2.207e+03 |
8.784e+73 |
5.991e+04 |
0 |
16 |
153 |
3.175e+03 |
4.827e+85 |
8.489e+04 |
0 |
17 |
171 |
4.709e+03 |
2.806e+98 |
1.418e+05 |
0 |
18 |
190 |
6.584e+03 |
2.805e+112 |
1.938e+05 |
0 |
19 |
210 |
9.484e+03 |
3.507e+127 |
3.213e+05 |
0 |
20 |
231 |
1.296e+04 |
8.788e+143 |
4.176e+05 |
0 |
21 |
253 |
1.819e+04 |
3.191e+161 |
6.794e+05 |
0 |
22 |
276 |
2.436e+04 |
2.661e+180 |
8.599e+05 |
0 |
23 |
300 |
3.342e+04 |
3.662e+200 |
1.327e+06 |
0 |
24 |
325 |
4.396e+04 |
1.305e+222 |
1.649e+06 |
0 |
25 |
351 |
5.918e+04 |
8.602e+244 |
2.552e+06 |
0 |
26 |
378 |
7.661e+04 |
1.634e+269 |
3.040e+06 |
0 |
27 |
406 |
1.014e+05 |
6.357e+294 |
4.651e+06 |
0 |
28 |
435 |
1.295e+05 |
Inf |
5.549e+06 |
0 |
29 |
465 |
1.688e+05 |
Inf |
8.146e+06 |
0 |
30 |
496 |
2.127e+05 |
Inf |
7.193e+06 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
CYIB like points: alpha=optimal
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.155e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
2.624e+00 |
4.823e+03 |
1.721e+01 |
0 |
4 |
15 |
3.234e+00 |
6.733e+06 |
2.498e+01 |
0 |
5 |
21 |
3.727e+00 |
9.003e+10 |
3.652e+01 |
0 |
6 |
28 |
4.328e+00 |
1.614e+16 |
4.752e+01 |
0 |
7 |
36 |
4.968e+00 |
3.243e+22 |
5.847e+01 |
0 |
8 |
45 |
5.492e+00 |
1.332e+30 |
8.050e+01 |
0 |
9 |
55 |
6.061e+00 |
7.866e+38 |
8.819e+01 |
0 |
10 |
66 |
6.778e+00 |
8.877e+48 |
1.111e+02 |
0 |
11 |
78 |
7.567e+00 |
1.766e+60 |
1.245e+02 |
0 |
12 |
91 |
8.327e+00 |
1.000e+73 |
1.161e+02 |
0 |
13 |
105 |
9.526e+00 |
8.569e+86 |
1.532e+02 |
0 |
14 |
120 |
1.072e+01 |
2.102e+102 |
1.903e+02 |
0 |
15 |
136 |
1.203e+01 |
1.217e+119 |
2.306e+02 |
0 |
16 |
153 |
1.382e+01 |
1.526e+137 |
2.231e+02 |
0 |
17 |
171 |
1.593e+01 |
4.720e+156 |
2.473e+02 |
0 |
18 |
190 |
1.814e+01 |
4.942e+177 |
3.124e+02 |
0 |
19 |
210 |
2.110e+01 |
1.017e+200 |
4.270e+02 |
0 |
20 |
231 |
2.465e+01 |
6.132e+223 |
3.929e+02 |
0 |
21 |
253 |
2.877e+01 |
1.117e+249 |
5.448e+02 |
0 |
22 |
276 |
3.354e+01 |
6.362e+275 |
6.860e+02 |
0 |
23 |
300 |
4.002e+01 |
7.364e+303 |
9.116e+02 |
0 |
24 |
325 |
4.736e+01 |
Inf |
1.003e+03 |
0 |
25 |
351 |
5.600e+01 |
Inf |
1.196e+03 |
0 |
26 |
378 |
6.716e+01 |
Inf |
1.221e+03 |
0 |
27 |
406 |
8.080e+01 |
Inf |
1.440e+03 |
0 |
28 |
435 |
9.673e+01 |
Inf |
1.796e+03 |
0 |
29 |
465 |
1.163e+02 |
Inf |
2.173e+03 |
0 |
30 |
496 |
1.412e+02 |
Inf |
2.785e+03 |
0 |
» SOURCE: A. Cuyt, I. Yaman, B.A. Ibrahimoglu and B. Benouahmane, Radial orthogonality and Lebesgue constants on the disk, Numer. Algo., 61 (2012), pp. 291-313.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
Good conditioning set (w.r.t. Zernike basis)
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
2.388e+00 |
7.862e-01 |
3.105e+00 |
0 |
2 |
6 |
3.307e+00 |
7.706e+00 |
5.353e+00 |
0 |
3 |
10 |
4.166e+00 |
4.568e+02 |
7.418e+00 |
0 |
4 |
15 |
4.901e+00 |
2.763e+05 |
1.745e+01 |
0 |
5 |
21 |
5.682e+00 |
1.475e+09 |
2.383e+01 |
0 |
6 |
28 |
6.422e+00 |
1.112e+14 |
2.256e+01 |
0 |
7 |
36 |
7.451e+00 |
9.768e+19 |
4.044e+01 |
0 |
8 |
45 |
8.384e+00 |
1.482e+27 |
5.479e+01 |
0 |
9 |
55 |
9.630e+00 |
3.201e+35 |
6.576e+01 |
0 |
10 |
66 |
1.090e+01 |
1.399e+45 |
7.467e+01 |
0 |
11 |
78 |
1.257e+01 |
1.009e+56 |
9.723e+01 |
0 |
12 |
91 |
1.434e+01 |
1.672e+68 |
1.057e+02 |
0 |
13 |
105 |
1.659e+01 |
5.123e+81 |
1.520e+02 |
0 |
14 |
120 |
1.891e+01 |
4.000e+96 |
1.240e+02 |
0 |
15 |
136 |
2.209e+01 |
6.332e+112 |
1.839e+02 |
0 |
16 |
153 |
2.578e+01 |
2.780e+130 |
2.444e+02 |
0 |
17 |
171 |
3.024e+01 |
2.665e+149 |
2.557e+02 |
0 |
18 |
190 |
3.528e+01 |
7.609e+169 |
3.316e+02 |
0 |
19 |
210 |
4.184e+01 |
5.042e+191 |
3.445e+02 |
0 |
20 |
231 |
4.971e+01 |
1.056e+215 |
4.357e+02 |
0 |
21 |
253 |
5.924e+01 |
5.397e+239 |
4.559e+02 |
0 |
22 |
276 |
7.037e+01 |
9.164e+265 |
5.741e+02 |
0 |
23 |
300 |
8.443e+01 |
3.963e+293 |
6.149e+02 |
0 |
24 |
325 |
1.016e+02 |
Inf |
7.708e+02 |
0 |
25 |
351 |
1.224e+02 |
Inf |
8.715e+02 |
0 |
26 |
378 |
1.472e+02 |
Inf |
1.090e+03 |
0 |
27 |
406 |
1.785e+02 |
Inf |
1.259e+03 |
0 |
28 |
435 |
2.166e+02 |
Inf |
1.558e+03 |
0 |
29 |
465 |
2.630e+02 |
Inf |
1.856e+03 |
0 |
30 |
496 |
3.187e+02 |
Inf |
2.268e+03 |
0 |
31 |
528 |
3.886e+02 |
Inf |
2.766e+03 |
0 |
32 |
561 |
4.740e+02 |
Inf |
3.336e+03 |
0 |
33 |
595 |
5.788e+02 |
Inf |
4.120e+03 |
0 |
34 |
630 |
7.055e+02 |
Inf |
5.129e+03 |
0 |
35 |
666 |
8.627e+02 |
Inf |
6.321e+03 |
0 |
36 |
703 |
1.056e+03 |
Inf |
8.002e+03 |
0 |
37 |
741 |
1.293e+03 |
Inf |
9.731e+03 |
0 |
38 |
780 |
1.582e+03 |
Inf |
1.245e+04 |
0 |
39 |
820 |
1.939e+03 |
Inf |
1.489e+04 |
0 |
40 |
861 |
2.376e+03 |
Inf |
1.924e+04 |
0 |
41 |
903 |
2.916e+03 |
Inf |
2.435e+04 |
0 |
42 |
946 |
3.574e+03 |
Inf |
3.046e+04 |
0 |
43 |
990 |
4.390e+03 |
Inf |
3.760e+04 |
0 |
44 |
1035 |
5.386e+03 |
Inf |
4.745e+04 |
0 |
45 |
1081 |
6.618e+03 |
Inf |
5.794e+04 |
0 |
46 |
1128 |
8.125e+03 |
Inf |
8.978e+04 |
0 |
47 |
1176 |
9.989e+03 |
Inf |
9.313e+04 |
0 |
48 |
1225 |
1.227e+04 |
Inf |
1.153e+05 |
0 |
49 |
1275 |
1.509e+04 |
Inf |
1.464e+05 |
0 |
50 |
1326 |
1.856e+04 |
Inf |
1.817e+05 |
0 |
» SOURCE: D. Ramos-Lopez, M.A. Sanchez-Granero, M. Fernandez-Martinez and A. Martinez Finkelstein, "Optimal sampling patterns for Zernike polynomials",Appl. Math. Comput.,274 (2016), pp. 247-257.
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
Gunzburger-Teckentrup
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.124e+00 |
0 |
2 |
6 |
1.989e+00 |
3.617e+01 |
7.861e+00 |
0 |
3 |
10 |
2.467e+00 |
4.301e+03 |
1.738e+01 |
0 |
4 |
15 |
3.050e+00 |
3.870e+06 |
2.207e+01 |
0 |
5 |
21 |
3.391e+00 |
4.540e+10 |
3.038e+01 |
0 |
6 |
28 |
3.855e+00 |
7.034e+15 |
4.440e+01 |
0 |
7 |
36 |
4.345e+00 |
1.567e+22 |
5.917e+01 |
0 |
8 |
45 |
4.852e+00 |
3.486e+29 |
7.172e+01 |
0 |
9 |
55 |
5.210e+00 |
2.419e+38 |
8.281e+01 |
0 |
10 |
66 |
5.696e+00 |
4.870e+48 |
1.036e+02 |
0 |
» SOURCE: M. Gunzburger and A. L. Teckentrup, "Optimal Point Sets for Total Degree Polynomial Interpolation in Moderate Dimensions"
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]
Almost optimal Lebesgue.
Deg. |
card |
Leb.Const. |
Abs.Det.Vand. |
Vand.Cond |
Out |
1 |
3 |
1.667e+00 |
1.866e+00 |
3.164e+00 |
0 |
2 |
6 |
1.989e+00 |
3.747e+01 |
7.657e+00 |
0 |
3 |
10 |
2.466e+00 |
4.309e+03 |
1.584e+01 |
0 |
4 |
15 |
2.959e+00 |
3.888e+06 |
2.262e+01 |
0 |
5 |
21 |
3.389e+00 |
4.530e+10 |
3.117e+01 |
0 |
6 |
28 |
3.852e+00 |
7.219e+15 |
3.545e+01 |
0 |
7 |
36 |
4.316e+00 |
1.482e+22 |
5.939e+01 |
0 |
8 |
45 |
4.761e+00 |
4.387e+29 |
6.257e+01 |
0 |
9 |
55 |
5.206e+00 |
2.510e+38 |
8.470e+01 |
0 |
10 |
66 |
5.667e+00 |
3.555e+48 |
9.653e+01 |
0 |
11 |
78 |
6.102e+00 |
1.050e+60 |
1.242e+02 |
0 |
12 |
91 |
6.564e+00 |
1.366e+73 |
1.298e+02 |
0 |
13 |
105 |
6.951e+00 |
2.812e+87 |
1.397e+02 |
0 |
14 |
120 |
7.521e+00 |
6.716e+102 |
1.964e+02 |
0 |
15 |
136 |
7.994e+00 |
1.494e+120 |
2.321e+02 |
0 |
16 |
153 |
8.353e+00 |
1.307e+139 |
2.245e+02 |
0 |
17 |
171 |
8.853e+00 |
2.439e+159 |
2.651e+02 |
0 |
18 |
190 |
9.207e+00 |
3.439e+181 |
3.001e+02 |
0 |
19 |
210 |
9.694e+00 |
7.999e+204 |
3.275e+02 |
0 |
20 |
231 |
1.017e+01 |
6.709e+229 |
3.737e+02 |
0 |
21 |
253 |
1.099e+01 |
1.906e+256 |
4.314e+02 |
0 |
22 |
276 |
1.149e+01 |
5.843e+284 |
4.395e+02 |
0 |
23 |
300 |
1.190e+01 |
Inf |
4.797e+02 |
0 |
24 |
325 |
1.228e+01 |
Inf |
5.401e+02 |
0 |
25 |
351 |
1.295e+01 |
Inf |
5.276e+02 |
0 |
26 |
378 |
1.452e+01 |
Inf |
5.769e+02 |
0 |
27 |
406 |
1.456e+01 |
Inf |
6.194e+02 |
0 |
28 |
435 |
1.531e+01 |
Inf |
6.199e+02 |
0 |
29 |
465 |
1.668e+01 |
Inf |
7.424e+02 |
0 |
30 |
496 |
1.760e+01 |
Inf |
7.587e+02 |
0 |
» SOURCE: G. Meurant and A. Sommariva, "On the computation of sets of points with Low Lebesgue constant on the unit disk"
» MATLAB FILE:
CARTESIAN COORDINATES: [.m]