Maximum Determinant (MD) 
Interpolation points on the Sphere S2

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Summary of data for Minimum Determinant (MD) points.

Caveat: All point sets are only approximate local optimizers of their respective criteria.
 
n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

  • Maximum determinant (MD) points, Degree n = 1, Number of points dn = 4
  • md01_0004pts.jpg
    md01_0004msh.jpg md01_0004int.jpg
    MD points
    n = 1, dn = 4
    Mesh norm function,
    h = 1.231
    Interpolation norm function,
    ||Ln|| = 2
    Eigenvalues of G
    lmin = 0.318, lavg = 0.318, lmax = 0.318
  • Maximum determinant (MD) points, Degree n = 2, Number of points dn = 9
  • md02_0009pts.jpg
    md02_0009msh.jpg md02_0009int.jpg
    MD points, 
    n = 2, dn = 9
    Mesh norm function,
    h = 0.818
    Interpolation norm function
    ||Ln|| = 3.24
    Eigenvalues of G
    lmin = 0.463, lavg = 0.716, lmax = 0.895 
  • Maximum determinant (MD) points, Degree n = 3, Number of points dn = 16
  • md03_0016pts.jpg
    md03_0016msh.jpg md03_0016int.jpg
    MD points,
    n = 3, dn = 16
    Mesh norm function,
    h = 0.575
    Interpolation norm function,
    ||Ln|| = 3.60
    Eigenvalues of G
    lmin = 0.797, lavg = 1.273, lmax = 1.915
  • Maximum determinant (MD) points, Degree n = 4, Number of points dn = 25
  • md04_0025pts.jpg
    md04_0025msh.jpg
    md04_0025int.jpg
    MD points
    n = 4, dn = 25
    Mesh norm function
    h = 0.518
    Interpolation norm function
    ||Ln|| = 5.22
     Eigenvalues of G
    lmin = 0.897, lavg = 1.989, lmax = 2.866

    Maximum determinant (MD) points, Degree n = 5, Number of points dn = 36
    md05_0036pts.jpg
    md05_0036msh.jpg
    md05_0036int.jpg
    md05_0036ev.jpg
    MD points
    n = 5, dn = 36
    Mesh norm function
    h = 0.439
    Interpolation norm function
    ||Ln|| = 6.20
     Eigenvalues of G
    lmin = 1.062, lavg = 2.865, lmax = 4.346

  • Maximum determinant (MD) points, Degree n = 6, Number of points dn = 49
  • md06_0049pts.jpg
    md06_0049msh.jpg
    md06_0049int.jpg
    MD points
    n = 6, dn = 49
    Mesh norm function
    h = 0.345
    Interpolation norm function
    ||Ln|| = 7.16
     Eigenvalues of G
    lmin = 1.034, lavg = 3.899, lmax = 6.162
  • Maximum determinant (MD) points, Degree n = 7, Number of points dn = 64
  • md07_0064pts.jpg
    md07_0064msh.jpg
    md07_0064int.jpg
    MD points
    n = 7, dn = 64
    Mesh norm function
    h = 0.308
    Interpolation norm function
    ||Ln|| = 8.19
     Eigenvalues of G
    lmin = 1.353, lavg = 5.093, lmax = 8.388
  • Maximum determinant (MD) points, Degree n = 8, Number of points dn = 81
  • md08_0081pts0.jpg md08_0081msh.jpg md08_0081int.jpg
    MD points
    n = 8, dn = 81
    Mesh norm function
    h = 0.280
    Interpolation norm function
    ||Ln|| = 8.86
     Eigenvalues of G
    lmin = 1.538, lavg = 6.446, lmax = 10.812
  • Maximum determinant (MD) points, Degree n = 9, Number of points dn = 100
  • md09_0100pts.jpg md09_0100msh.jpg md09_0100int.jpg
    MD points
    n = 9, dn = 100
    Mesh norm function
    h = 0.236
    Interpolation norm function
    ||Ln|| = 8.61
     Eigenvalues of G
    lmin = 1.788, lavg = 7.958, lmax = 13.593
  • Maximum determinant (MD) points, Degree n = 10, Number of points dn = 121
  • md10_0121pts.jpg md10_0121msh.jpg md10_0121int.jpg md10_0121ev.jpg
    MD points
    n = 10, dn = 121
    Mesh norm function
    h = 0.234
    Interpolation norm function
    ||Ln|| = 11.84
     Eigenvalues of G
    lmin = 1.958, lavg = 9.629, lmax = 16.425
  • Maximum determinant (MD) points, Degree n = 11, Number of points dn = 144
  • md11_0144pts.jpg md11_0144msh.jpg md11_0144int.jpg md11_0144ev.jpg
    MD points
    n = 11, dn = 144
    Mesh norm function
    h = 0.224
    Interpolation norm function
    ||Ln|| = 14.05
     Eigenvalues of G
    lmin = 1.733, lavg = 11.459, lmax = 20.087
  • Maximum determinant (MD) points, Degree n = 12, Number of points dn = 169
  • md12_0169pts.jpg md12_0169msh.jpg md12_0169int.jpg md12_0169ev.jpg
    MD points
    n = 12, dn = 169
    Mesh norm function
    h = 0.210
    Interpolation norm function
    ||Ln|| = 14.70
     Eigenvalues of G
    lmin = 2.327, lavg = 13.449, lmax = 23.255
  • Maximum determinant (MD) points, Degree n = 13, Number of points dn = 196
  • md13_0196pts.jpg md13_0196msh.jpg md13_0196int.jpg md13_0196ev.jpg
    MD points
    n = 13, dn = 196
    Mesh norm function
    h = 0.181
    Interpolation norm function
    ||Ln|| = 15.16
     Eigenvalues of G
    lmin = 2.045, lavg = 15.597, lmax = 27.608
  • Maximum determinant (MD) points, Degree n = 14, Number of points dn = 225
  • md14_0225pts.jpg md14_0225msh.jpg md14_0225int.jpg md14_0225ev.jpg
    MD points
    n = 14, dn = 225
    Mesh norm function
    h = 0.176
    Interpolation norm function
    ||Ln|| = 17.81
     Eigenvalues of G
    lmin = 2.288, lavg = 17.905, lmax = 32.119
  • Maximum determinant (MD) points, Degree n = 15, Number of points dn = 256
  • md15_0256pts.jpg md15_0256msh.jpg md15_0256int.jpg md15_0256ev.jpg
    MD points
    n = 15, dn = 256
    Mesh norm function
    h = 0.161
    Interpolation norm function
    ||Ln|| = 18.08
     Eigenvalues of G
    lmin = 2.321, lavg = 20.372, lmax = 36.687
  • Maximum determinant (MD) points, Degree n = 16, Number of points dn = 289
  • md16_0289pts.jpg md16_0289msh.jpg md16_0289int.jpg md16_0289ev.jpg
    MD points
    n = 16, dn = 289
    Mesh norm function
    h = 0.157
    Interpolation norm function
    ||Ln|| = 19.92
     Eigenvalues of G
    lmin = 2.724, lavg = 22.998, lmax = 40.970
  • Maximum determinant (MD) points, Degree n = 17, Number of points dn = 324
  • md17_0324pts.jpg md17_0324msh.jpg md17_0324int.jpg md17_0324ev.jpg
    MD points
    n = 17, dn = 324
    Mesh norm function
    h = 0.147
    Interpolation norm function
    ||Ln|| = 21.55
     Eigenvalues of G
    lmin = 2.562, lavg = 25.783, lmax = 45.959
  • Maximum determinant (MD) points, Degree n = 18, Number of points dn = 361
  • md18_0361pts.jpg md18_0361msh.jpg md18_0361int.jpg md18_0361ev.jpg
    MD points
    n = 18, dn = 361
    Mesh norm function
    h =0.140
    Interpolation norm function
    ||Ln|| = 21.08
     Eigenvalues of G
    lmin = 3.074, lavg = 28.727, lmax = 52.078
  • Maximum determinant (MD) points, Degree n = 19, Number of points dn = 400
  • md19_0400pts.jpg md19_0400msh.jpg md19_0400int.jpg md19_0400ev.jpg
    MD points
    n = 19, dn = 400
    Mesh norm function
    h = 0.132
    Interpolation norm function
    ||Ln|| = 23.64
     Eigenvalues of G
    lmin = 2.973, lavg = 31.831, lmax = 58.300
  • Maximum determinant (MD) points, Degree n = 20, Number of points dn = 441
  • md20_0441pts.jpg md20_0441msh.jpg md20_0441int.jpg md20_0441ev.jpg
    MD points
    n = 20, dn = 441
    Mesh norm function
    h = 0.125
    Interpolation norm function
    ||Ln|| = 24.66
     Eigenvalues of G
    lmin = 2.924, lavg = 35.094, lmax = 63.669
  • Maximum determinant (MD) points, Degree n = 21, Number of points dn = 484
  • md21_0484pts.jpg md21_0484msh.jpg md21_0484int.jpg md21_0484ev.jpg
    MD points
    n = 21, dn = 484
    Mesh norm function
    h = 0.120
    Interpolation norm function
    ||Ln|| = 23.83
     Eigenvalues of G
    lmin = 3.597, lavg =  38.515, lmax = 70.130
  • Maximum determinant (MD) points, Degree n = 22, Number of points dn = 529
  • md22_0529pts.jpg md22_0529msh.jpg md22_0529int.jpg md22_0529ev.jpg
    MD points
    n = 22, dn = 529
    Mesh norm function
    h = 0.114
    Interpolation norm function
    ||Ln|| = 25.25
     Eigenvalues of G
    lmin = 3.460, lavg = 42.096, lmax = 76.522
  • Maximum determinant (MD) points, Degree n = 23, Number of points dn = 576
  • md23_0576pts.jpg md23_0576msh.jpg md23_0576int.jpg md23_0576ev.jpg
    MD points
    n = 23, dn = 576
    Mesh norm function
    h = 0.112
    Interpolation norm function
    ||Ln|| = 28.70
     Eigenvalues of G
    lmin = 3.211, lavg = 45.837, lmax = 83.703
  • Maximum determinant (MD) points, Degree n = 24, Number of points dn = 625
  • md24_0625pts.jpg md24_0625msh.jpg md24_0625int.jpg md24_0625ev.jpg
    MD points
    n = 24, dn = 625
    Mesh norm function
    h = 0.103
    Interpolation norm function
    ||Ln|| = 28.41
     Eigenvalues of G
    lmin = 3.324, lavg = 49.736, lmax = 91.704
  • Maximum determinant (MD) points, Degree n = 25, Number of points dn = 676
  • md25_0676pts.jpg md25_0676msh.jpg md25_0676int.jpg md25_0676ev.jpg
    MD points
    n = 25, dn = 676
    Mesh norm function
    h = 0.101
    Interpolation norm function
    ||Ln|| = 31.15
     Eigenvalues of G
    lmin = 3.631, lavg = 53.794 , lmax = 98.977
  • Maximum determinant (MD) points, Degree n = 26, Number of points dn = 729
  • md26_0729pts.jpg md26_0729msh.jpg md26_0729int.jpg md26_0729ev.jpg
    MD points
    n = 26, dn = 729
    Mesh norm function
    h = 0.095
    Interpolation norm function
    ||Ln|| = 31.21
     Eigenvalues of G
    lmin = 3.430, lavg = 58.012, lmax = 106.770
  • Maximum determinant (MD) points, Degree n = 27, Number of points dn = 784
  • md27_0784pts.jpg md27_0784msh.jpg md27_0784int.jpg md27_0784ev.jpg
    MD points
    n = 27, dn = 784
    Mesh norm function
    h = 0.095
    Interpolation norm function
    ||Ln|| = 32.31
     Eigenvalues of G
    lmin = 4.007, lavg = 62.389, lmax = 114.840
  • Maximum determinant (MD) points, Degree n = 28, Number of points dn = 841
  • md28_0841pts.jpg md28_0841msh.jpg md28_0841int.jpg md28_0841ev.jpg
    MD points
    n = 28, dn = 841
    Mesh norm function
    h = 0.092
    Interpolation norm function
    ||Ln|| = 33.92
     Eigenvalues of G
    lmin = 3.283, lavg = 66.925, lmax = 125.928
  • Maximum determinant (MD) points, Degree n = 29, Number of points dn = 900
  • md29_0900pts.jpg md29_0900msh.jpg md29_0900int.jpg md29_0900ev.jpg
    MD points
    n = 29, dn = 900
    Mesh norm function
    h = 0.089
    Interpolation norm function
    ||Ln|| = 36.98
     Eigenvalues of G
    lmin = 4.033, lavg = 71.620, lmax = 132.464

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    Rob Womersley, School of Mathematics, UNSW. Last updated 3-Nov-1999