Maximum Smallest Eigenvalue (EV)
Interpolation points on the Sphere S2

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Summary of data for Maximum Smallest Eigenvalue (EV) points.
 
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  • Maximum smallest eigenvalue (EV) points, Degree n = 1, Number of points dn = 4
  • ev01_0004pts.jpg
    ev01_0004msh.jpg ev01_0004int.jpg
    EV 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
  • Maximum smallest eigenvalue (EV) points, Degree n = 2, Number of points dn = 9
  • ev02_0009pts.jpg
    ev02_0009msh.jpg ev02_0009int.jpg
    EV points, 
    n = 2, dn = 9
    Mesh norm function,
    h = 0.842
    Interpolation norm function
    ||Ln|| = 3.34
    Eigenvalues of G
    lmin = 0.509, lavg = 0.716, lmax = 0.889
  • Maximum smallest eigenvalue (EV) points, Degree n = 3, Number of points dn = 16
  • ev03_0016pts.jpg
    ev03_0016msh.jpg ev03_0016int.jpg
    EV points,
    n = 3, dn = 16
    Mesh norm function,
    h = 0.598
    Interpolation norm function,
    ||Ln|| = 3.57
    Eigenvalues of G
    lmin = 0.825, lavg = 1.273, lmax = 2.307
  • Maximum smallest eigenvalue (EV) points, Degree n = 4, Number of points dn = 25
  • ev04_0025pts.jpg
    ev04_0025msh.jpg
    ev04_0025int.jpg
    EV points
    n = 4, dn = 25
    Mesh norm function
    h = 0.517
    Interpolation norm function
    ||Ln|| = 5.12
     Eigenvalues of G
    lmin = 1.112, lavg = 1.989, lmax = 3.257

    Maximum smallest eigenvalue (EV) points, Degree n = 5, Number of points dn = 36
    ev05_0036pts.jpg
    ev05_0036msh.jpg
    ev05_0036int.jpg
    ev05_0036ev.jpg
    EV points
    n = 5, dn = 36
    Mesh norm function
    h = 0.442
    Interpolation norm function
    ||Ln|| = 6.13
     Eigenvalues of G
    lmin = 1.507, lavg = 2.865, lmax = 4.857

  • Maximum smallest eigenvalue (EV) points, Degree n = 6, Number of points dn = 49
  • ev06_0049pts.jpg
    ev06_0049msh.jpg
    ev06_0049int.jpg
    EV points
    n = 6, dn = 49
    Mesh norm function
    h = 0.386
    Interpolation norm function
    ||Ln|| = 7.35
     Eigenvalues of G
    lmin = 1.839, lavg = 3.899, lmax = 6.465
  • Maximum smallest eigenvalue (EV) points, Degree n = 7, Number of points dn = 64
  • ev07_0064pts.jpg
    ev07_0064msh.jpg
    ev07_0064int.jpg
    EV points
    n = 7, dn = 64
    Mesh norm function
    h = 0.328
    Interpolation norm function
    ||Ln|| = 7.67
     Eigenvalues of G
    lmin = 2.154, lavg = 5.093, lmax = 8.503
  • Maximum smallest eigenvalue (EV) points, Degree n = 8, Number of points dn = 81
  • ev08_0081pts0.jpg ev08_0081msh.jpg ev08_0081int.jpg
    EV points
    n = 8, dn = 81
    Mesh norm function
    h = 0.295
    Interpolation norm function
    ||Ln|| = 9.13
     Eigenvalues of G
    lmin = 2.583, lavg = 6.446, lmax = 10.88
  • Maximum smallest eigenvalue (EV) points, Degree n = 9, Number of points dn = 100
  • ev09_0100pts.jpg ev09_0100msh.jpg ev09_0100int.jpg
    EV points
    n = 9, dn = 100
    Mesh norm function
    h = 0.271
    Interpolation norm function
    ||Ln|| = 10.03
     Eigenvalues of G
    lmin = 2.959, lavg = 7.958, lmax = 14.02
  • Maximum smallest eigenvalue (EV) points, Degree n = 10, Number of points dn = 121
  • ev10_0121pts.jpg ev10_0121msh.jpg ev10_0121int.jpg ev10_0121ev.jpg
    EV points
    n = 10, dn = 121
    Mesh norm function
    h = 0.254
    Interpolation norm function
    ||Ln|| = 11.31
     Eigenvalues of G
    lmin = 3.444, lavg = 9.629, lmax = 16.76
  • Maximum smallest eigenvalue (EV) points, Degree n = 11, Number of points dn = 144
  • ev11_0144pts.jpg ev11_0144msh.jpg ev11_0144int.jpg ev11_0144ev.jpg
    EV points
    n = 11, dn = 144
    Mesh norm function
    h = 0.228
    Interpolation norm function
    ||Ln|| = 12.03
     Eigenvalues of G
    lmin = 3.857, lavg = 11.46, lmax = 20.16
  • Maximum smallest eigenvalue (EV) points, Degree n = 12, Number of points dn = 169
  • ev12_0169pts.jpg ev12_0169msh.jpg ev12_0169int.jpg ev12_0169ev.jpg
    EV points
    n = 12, dn = 169
    Mesh norm function
    h = 0.213
    Interpolation norm function
    ||Ln|| = 13.64
     Eigenvalues of G
    lmin = 4.312, lavg = 13.45, lmax = 23.87
  • Maximum smallest eigenvalue (EV) points, Degree n = 13, Number of points dn = 196
  • ev13_0196pts.jpg ev13_0196msh.jpg ev13_0196int.jpg ev13_0196ev.jpg
    EV points
    n = 13, dn = 196
    Mesh norm function
    h = 0.198
    Interpolation norm function
    ||Ln|| = 13.74
     Eigenvalues of G
    lmin = 4.698, lavg = 15.60, lmax = 28.57
  • Maximum smallest eigenvalue (EV) points, Degree n = 14, Number of points dn = 225
  • ev14_0225pts.jpg ev14_0225msh.jpg ev14_0225int.jpg ev14_0225ev.jpg
    EV points
    n = 14, dn = 225
    Mesh norm function
    h = 0.185
    Interpolation norm function
    ||Ln|| = 15.27
     Eigenvalues of G
    lmin = 5.303, lavg = 17.91, lmax = 32.33
  • Maximum smallest eigenvalue (EV) points, Degree n = 15, Number of points dn = 256
  • ev15_0256pts.jpg ev15_0256msh.jpg ev15_0256int.jpg ev15_0256ev.jpg
    EV points
    n = 15, dn = 256
    Mesh norm function
    h = 0.177
    Interpolation norm function
    ||Ln|| = 16.74
     Eigenvalues of G
    lmin = 5.699, lavg = 20.37, lmax = 37.34
  • Maximum smallest eigenvalue (EV) points, Degree n = 16, Number of points dn = 289
  • ev16_0289pts.jpg ev16_0289msh.jpg ev16_0289int.jpg ev16_0289ev.jpg
    EV points
    n = 16, dn = 289
    Mesh norm function
    h = 0.171
    Interpolation norm function
    ||Ln|| = 16.81
     Eigenvalues of G
    lmin = 6.185, lavg = 23.00, lmax = 41.62
  • Maximum smallest eigenvalue (EV) points, Degree n = 17, Number of points dn = 324
  • ev17_0324pts.jpg ev17_0324msh.jpg ev17_0324int.jpg ev17_0324ev.jpg
    EV points
    n = 17, dn = 324
    Mesh norm function
    h = 0.158
    Interpolation norm function
    ||Ln|| = 18.15
     Eigenvalues of G
    lmin = 6.610, lavg = 25.78, lmax = 48.02
  • Maximum smallest eigenvalue (EV) points, Degree n = 18, Number of points dn = 361
  • ev18_0361pts.jpg ev18_0361msh.jpg ev18_0361int.jpg ev18_0361ev.jpg
    EV points
    n = 18, dn = 361
    Mesh norm function
    h = 0.150
    Interpolation norm function
    ||Ln|| = 18.85
     Eigenvalues of G
    lmin = 7.131, lavg = 28.73, lmax = 56.06
  • Maximum smallest eigenvalue (EV) points, Degree n = 19, Number of points dn = 400
  • ev19_0400pts.jpg ev19_0400msh.jpg ev19_0400int.jpg ev19_0400ev.jpg
    EV points
    n = 19, dn = 400
    Mesh norm function
    h = 0.146
    Interpolation norm function
    ||Ln|| = 19.64
     Eigenvalues of G
    lmin = 7.846, lavg = 31.83, lmax = 61.15
  • Maximum smallest eigenvalue (EV) points, Degree n = 20, Number of points dn = 441
  • ev20_0441pts.jpg ev20_0441msh.jpg ev20_0441int.jpg ev20_0441ev.jpg
    EV points
    n = 20, dn = 441
    Mesh norm function
    h = 0.137
    Interpolation norm function
    ||Ln|| = 19.73
     Eigenvalues of G
    lmin = 8.155, lavg = 35.09, lmax = 65.74
  • Maximum smallest eigenvalue (EV) points, Degree n = 21, Number of points dn = 484
  • ev21_0484pts.jpg ev21_0484msh.jpg ev21_0484int.jpg ev21_0484ev.jpg
    EV points
    n = 21, dn = 484
    Mesh norm function
    h = 0.135
    Interpolation norm function
    ||Ln|| = 22.19
     Eigenvalues of G
    lmin = 8.846, lavg =  38.52, lmax = 77.58
  • Maximum smallest eigenvalue (EV) points, Degree n = 22, Number of points dn = 529
  • ev22_0529pts.jpg ev22_0529msh.jpg ev22_0529int.jpg ev22_0529ev.jpg
    EV points
    n = 22, dn = 529
    Mesh norm function
    h = 0.130
    Interpolation norm function
    ||Ln|| = 22.69
     Eigenvalues of G
    lmin = 9.228, lavg = 42.10, lmax = 78.81
  • Maximum smallest eigenvalue (EV) points, Degree n = 23, Number of points dn = 576
  • ev23_0576pts.jpg ev23_0576msh.jpg ev23_0576int.jpg ev23_0576ev.jpg
    EV points
    n = 23, dn = 576
    Mesh norm function
    h = 0.124
    Interpolation norm function
    ||Ln|| = 24.45
     Eigenvalues of G
    lmin = 10.00, lavg = 45.837, lmax = 84.954
  • Maximum smallest eigenvalue (EV) points, Degree n = 24, Number of points dn = 625
  • ev24_0625pts.jpg ev24_0625msh.jpg ev24_0625int.jpg ev24_0625ev.jpg
    EV points
    n = 24, dn = 625
    Mesh norm function
    h = 0.118
    Interpolation norm function
    ||Ln|| = 24.45
     Eigenvalues of G
    lmin = 10.48, lavg = 49.74, lmax = 95.77
  • Maximum smallest eigenvalue (EV) points, Degree n = 25, Number of points dn = 676
  • ev25_0676pts.jpg ev25_0676msh.jpg ev25_0676int.jpg ev25_0676ev.jpg
    EV points
    n = 25, dn = 676
    Mesh norm function
    h = 0.113
    Interpolation norm function
    ||Ln|| = 26.02
     Eigenvalues of G
    lmin = 10.57, lavg = 53.79 , lmax = 104.1
  • Maximum smallest eigenvalue (EV) points, Degree n = 26, Number of points dn = 729
  • ev26_0729pts.jpg ev26_0729msh.jpg ev26_0729int.jpg ev26_0729ev.jpg
    EV points
    n = 26, dn = 729
    Mesh norm function
    h = 0.106
    Interpolation norm function
    ||Ln|| = 26.22
     Eigenvalues of G
    lmin = 10.56, lavg = 58.01, lmax = 110.4
  • Maximum smallest eigenvalue (EV) points, Degree n = 27, Number of points dn = 784
  • ev27_0784pts.jpg ev27_0784msh.jpg ev27_0784int.jpg ev27_0784ev.jpg
    EV points
    n = 27, dn = 784
    Mesh norm function
    h = 0.106
    Interpolation norm function
    ||Ln|| = 27.36
     Eigenvalues of G
    lmin = 11.60, lavg = 62.39, lmax = 116.1
  • Maximum smallest eigenvalue (EV) points, Degree n = 28, Number of points dn = 841
  • ev28_0841pts.jpg ev28_0841msh.jpg ev28_0841int.jpg ev28_0841ev.jpg
    EV points
    n = 28, dn = 841
    Mesh norm function
    h = 0.100
    Interpolation norm function
    ||Ln|| = 28.97
     Eigenvalues of G
    lmin = 11.72, lavg = 66.93, lmax = 131.1
  • Maximum smallest eigenvalue (EV) points, Degree n = 29, Number of points dn = 900
  • ev29_0900pts.jpg ev29_0900msh.jpg ev29_0900int.jpg ev29_0900ev.jpg
    EV points
    n = 29, dn = 900
    Mesh norm function
    h = 0.097
    Interpolation norm function
    ||Ln|| = 29.94
     Eigenvalues of G
    lmin = 13.56, lavg = 71.62, lmax = 136.2

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    Rob Womersley, School of Mathematics, UNSW. Last updated 15-Sep-1999