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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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: