# 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
•  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
•  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
•  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
•  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
 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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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
•  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