Minimum Energy (ME)
Interpolation points on the Sphere S2

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Summary of data for Minimum Energy (ME) points.
 
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

  • Minimum energy (ME) points, Degree n = 1, Number of points dn = 4
  • me01_0004pts.jpg
    me01_0004msh.jpg me01_0004int.jpg
    ME points
    n = 1, dn = 4
    Mesh norm function,
    h = 1.2
    Interpolation norm function,
    ||Ln|| = 2.00
    Eigenvalues of G
    lmin = 0.318, lavg = 0.318, lmax = 0.318
  • Minimum energy (ME) points, Degree n = 2, Number of points dn = 9
  • me02_0009pts.jpg
    me02_0009msh.jpg me02_0009int.jpg
    ME points, 
    n = 2, dn = 9
    Mesh norm function,
    h = 0.806
    Interpolation norm function
    ||Ln|| = 3.19
    Eigenvalues of G
    lmin = 0.439, lavg = 0.716, lmax = 0.895
  • Minimum energy (ME) points, Degree n = 3, Number of points dn = 16
  • me03_0016pts.jpg
    me03_0016msh.jpg me03_0016int.jpg
    ME points,
    n = 3, dn = 16
    Mesh norm function,
    h = 0.580
    Interpolation norm function,
    ||Ln|| = 3.67
    Eigenvalues of G
    lmin = 0.708, lavg = 1.273, lmax = 1.809
  • Minimum energy (ME) points, Degree n = 4, Number of points dn = 25
  • me04_0025pts.jpg
    me04_0025msh.jpg
    me04_0025int.jpg
    ME points
    n = 4, dn = 25
    Mesh norm function
    h = 0.520
    Interpolation norm function
    ||Ln|| = 5.60
     Eigenvalues of G
    lmin = 0.629, lavg = 1.989, lmax = 3.155

    Minimum energy (ME) points, Degree n = 5, Number of points dn = 36
    me05_0036pts.jpg
    me05_0036msh.jpg
    me05_0036int.jpg
    me05_0036ev.jpg
    ME points
    n = 5, dn = 36
    Mesh norm function
    h = 0.412
    Interpolation norm function
    ||Ln|| = 7.59
     Eigenvalues of G
    lmin = 0.463, lavg = 2.865, lmax = 5.129

  • Minimum energy (ME) points, Degree n = 6, Number of points dn = 49
  • me06_0049pts.jpg
    me06_0049msh.jpg
    me06_0049int.jpg
    ME points
    n = 6, dn = 49
    Mesh norm function
    h = 0.349 
    Interpolation norm function
    ||Ln|| = 7.39
     Eigenvalues of G
    lmin = 0.545, lavg = 3.899, lmax = 6.962
  • Minimum energy (ME) points, Degree n = 7, Number of points dn = 64
  • me07_0064pts.jpg
    me07_0064msh.jpg
    me07_0064int.jpg
    ME points
    n = 7, dn = 64
    Mesh norm function
    h = 0.304
    Interpolation norm function
    ||Ln|| = 12.54
     Eigenvalues of G
    lmin = 0.251, lavg = 5.093, lmax = 9.854
  • Minimum energy (ME) points, Degree n = 8, Number of points dn = 81
  • me08_0081pts0.jpg me08_0081msh.jpg me08_0081int.jpg
    ME points
    n = 8, dn = 81
    Mesh norm function
    h = 0.272
    Interpolation norm function
    ||Ln|| = 12.92
     Eigenvalues of G
    lmin = 0.371, lavg = 6.446, lmax = 12.43
  • Minimum energy (ME) points, Degree n = 9, Number of points dn = 100
  • me09_0100pts.jpg me09_0100msh.jpg me09_0100int.jpg
    ME points
    n = 9, dn = 100
    Mesh norm function
    h = 0.244
    Interpolation norm function
    ||Ln|| = 9.96
     Eigenvalues of G
    lmin = 1.042, lavg = 7.958, lmax = 14.65
  • Minimum energy (ME) points, Degree n = 10, Number of points dn = 121
  • me10_0121pts.jpg me10_0121msh.jpg me10_0121int.jpg me10_0121ev.jpg
    ME points
    n = 10, dn = 121
    Mesh norm function
    h = 0.340
    Interpolation norm function
    ||Ln|| = 161.8
     Eigenvalues of G
    lmin = 0.0026, lavg = 9.629, lmax = 19.31
  • Minimum energy (ME) points, Degree n = 11, Number of points dn = 144
  • me11_0144pts.jpg me11_0144msh.jpg me11_0144int.jpg me11_0144ev.jpg
    ME points
    n = 11, dn = 144
    Mesh norm function
    h = 0.208
    Interpolation norm function
    ||Ln|| = 373.9
     Eigenvalues of G
    lmin = 0.0006, lavg = 11.46, lmax = 22.86
  • Minimum energy (ME) points, Degree n = 12, Number of points dn = 169
  • me12_0169pts.jpg me12_0169msh.jpg me12_0169int.jpg me12_0169ev.jpg
    ME points
    n = 12, dn = 169
    Mesh norm function
    h = 0.183.
    Interpolation norm function
    ||Ln|| = 1504.8
     Eigenvalues of G
    lmin = 0.00005, lavg = 13.45, lmax = 26.86
  • Minimum energy (ME) points, Degree n = 13, Number of points dn = 196
  • me13_0196pts.jpg me13_0196msh.jpg me13_0196int.jpg me13_0196ev.jpg
    ME points
    n = 13, dn = 196
    Mesh norm function
    h = 0.172
    Interpolation norm function
    ||Ln|| = 422.1
     Eigenvalues of G
    lmin = 0.0007, lavg = 15.60, lmax = 31.26
  • Minimum energy (ME) points, Degree n = 14, Number of points dn = 225
  • me14_0225pts.jpg me14_0225msh.jpg me14_0225int.jpg me14_0225ev.jpg
    ME points
    n = 14, dn = 225
    Mesh norm function
    h = 0.164
    Interpolation norm function
    ||Ln|| = 172.6
     Eigenvalues of G
    lmin = 0.0062, lavg = 17.90, lmax = 35.79
  • Minimum energy (ME) points, Degree n = 15, Number of points dn = 256
  • me15_0256pts.jpg me15_0256msh.jpg me15_0256int.jpg me15_0256ev.jpg
    ME points
    n = 15, dn = 256
    Mesh norm function
    h = 0.156
    Interpolation norm function
    ||Ln|| = 267.1
     Eigenvalues of G
    lmin = 0.0035, lavg = 20.37, lmax = 40.73
  • Minimum energy (ME) points, Degree n = 16, Number of points dn = 289
  • me16_0289pts.jpg me16_0289msh.jpg me16_0289int.jpg me16_0289ev.jpg
    ME points
    n = 16, dn = 289
    Mesh norm function
    h = 0.144
    Interpolation norm function
    ||Ln|| = 162.1
     Eigenvalues of G
    lmin = 0.0099, lavg = 23.00, lmax = 45.86
  • Minimum energy (ME) points, Degree n = 17, Number of points dn = 324
  • me17_0324pts.jpg me17_0324msh.jpg me17_0324int.jpg me17_0324ev.jpg
    ME points
    n = 17, dn = 324
    Mesh norm function
    h = 0.142
    Interpolation norm function
    ||Ln|| = 1968.0
     Eigenvalues of G
    lmin = 0.00007, lavg = 25.78, lmax = 51.57
  • Minimum energy (ME) points, Degree n = 18, Number of points dn = 361
  • me18_0361pts.jpg me18_0361msh.jpg me18_0361int.jpg me18_0361ev.jpg
    ME points
    n = 18, dn = 361
    Mesh norm function
    h = 0.138
    Interpolation norm function
    ||Ln|| = 2101.6
     Eigenvalues of G
    lmin = 0.0004, lavg = 28.73, lmax = 57.38
  • Minimum energy (ME) points, Degree n = 19, Number of points dn = 400
  • me19_0400pts.jpg me19_0400msh.jpg me19_0400int.jpg me19_0400ev.jpg
    ME points
    n = 19, dn = 400
    Mesh norm function
    h = 0.126
    Interpolation norm function
    ||Ln|| = 1138.4
     Eigenvalues of G
    lmin = 0.0004, lavg = 31.83, lmax = 63.67
  • Minimum energy (ME) points, Degree n = 20, Number of points dn = 441
  • me20_0441pts.jpg me20_0441msh.jpg me20_0441int.jpg me20_0441ev.jpg
    ME points
    n = 20, dn = 441
    Mesh norm function
    h = 0.119
    Interpolation norm function
    ||Ln|| = 29565.2
     Eigenvalues of G
    lmin = 0.000001, lavg = 35.09, lmax = 70.22
  • Minimum energy (ME) points, Degree n = 21, Number of points dn = 484
  • me21_0484pts.jpg me21_0484msh.jpg me21_0484int.jpg me21_0484ev.jpg
    ME points
    n = 21, dn = 484
    Mesh norm function
    h = 0.115
    Interpolation norm function
    ||Ln|| = 793.1
     Eigenvalues of G
    lmin = 0.00094, lavg = 38.52, lmax = 77.10
  • Minimum energy (ME) points, Degree n = 22, Number of points dn = 529
  • me22_0529pts.jpg me22_0529msh.jpg me22_0529int.jpg me22_0529ev.jpg
    ME points
    n = 22, dn = 529
    Mesh norm function
    h = 0.108
    Interpolation norm function
    ||Ln|| = 1569.3
     Eigenvalues of G
    lmin = 0.00023, lavg = 42.10, lmax = 84.13
  • Minimum energy (ME) points, Degree n = 23, Number of points dn = 576
  • me23_0576pts.jpg me23_0576msh.jpg me23_0576int.jpg me23_0576ev.jpg
    ME points
    n = 23, dn = 576
    Mesh norm function
    h = 0.104
    Interpolation norm function
    ||Ln|| = 1369.5
     Eigenvalues of G
    lmin = 0.00053, lavg = 45.84, lmax = 91.78
  • Minimum energy (ME) points, Degree n = 24, Number of points dn = 625
  • me24_0625pts.jpg me24_0625msh.jpg me24_0625int.jpg me24_0625ev.jpg
    ME points
    n = 24, dn = 625
    Mesh norm function
    h = 0.103
    Interpolation norm function
    ||Ln|| = 5106.1
     Eigenvalues of G
    lmin = 0.000032, lavg = 49.74, lmax = 99.52
  • Minimum energy (ME) points, Degree n = 25, Number of points dn = 676
  • me25_0676pts.jpg me25_0676msh.jpg me25_0676int.jpg me25_0676ev.jpg
    ME points
    n = 25, dn = 676
    Mesh norm function
    h = 0.097
    Interpolation norm function
    ||Ln|| = 2109.8
     Eigenvalues of G
    lmin = 0.00024, lavg = 53.79, lmax = 107.8
  • Minimum energy (ME) points, Degree n = 26, Number of points dn = 729
  • me26_0729pts.jpg me26_0729msh.jpg me26_0729int.jpg me26_0729ev.jpg
    ME points
    n = 26, dn = 729
    Mesh norm function
    h = 0.094
    Interpolation norm function
    ||Ln|| = 9615.7
    Eigenvalues of G
    lmin = 0.000015, lavg = 58.01, lmax = 116.2
  • Minimum energy (ME) points, Degree n = 27, Number of points dn = 784
  • me27_0784pts.jpg me27_0784msh.jpg me27_0784int.jpg me27_0784ev.jpg
    ME points
    n = 27, dn = 784
    Mesh norm function
    h = 0.090
    Interpolation norm function
    ||Ln|| = 20224.5
     Eigenvalues of G
    lmin = 0.000003, lavg = 62.39, lmax = 124.8
  • Minimum energy (ME) points, Degree n = 28, Number of points dn = 841
  • me28_0841pts.jpg me28_0841msh.jpg me28_0841int.jpg me28_0841ev.jpg
    ME points
    n = 28, dn = 841
    Mesh norm function
    h = 0.085
    Interpolation norm function
    ||Ln|| = 878.4
     Eigenvalues of G
    lmin = 0.0020, lavg = 66.93, lmax = 133.9
  • Minimum energy (ME) points, Degree n = 29, Number of points dn = 900
  • me29_0900pts.jpg me29_0900msh.jpg me29_0900int.jpg me29_0900ev.jpg
    ME points
    n = 29, dn = 900
    Mesh norm function
    h = 0.084
    Interpolation norm function
    ||Ln|| = 2127.4
     Eigenvalues of G
    lmin = 0.00026, lavg = 71.62, lmax = 143.4

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