Eigenvalue (EV)
Interpolation points on the Sphere S2

Notation, and comparisons of different point sets.

The Points data files each have four columns corresponding to the x, y, and z coordinates of the points,
plus a fourth column giving the weight for that point in the quadrature rule.

Caveat: All point sets are only approximate local optimizers of their respective criteria.

Maximum Smallest Eigenvalue (EV) points

n
dn
Points
Images
(JPEG)
h
||Ln||
lmin
lavg
lmax
R
log det G
|| G-1 ||1
PE
1
4
ev01.0004
ev01_0004
1.231
2.00
0.318
0.318
0.318
2.00
-4.58
3.14
3.67
2
9
ev02.0009
 ev02_0009
0.842
3.34
0.825
0.716
0.889
3.56
-3.23
2.28
25.78
3
16
ev03.0016
ev03_0016
0.598
3.57
1.112
1.273
2.307
4.97
3.12
1.68
93.34
4
25
ev04.0025
ev04_0025
0.517
5.12
1.112
1.989
3.257
6.69
15.75
1.61
244.53
5
36
ev05.0036
ev05_0036
0.442
6.13
1.507
2.865
4.857
8.27
35.36
1.29
530.84
6
49
ev06.0049
ev06_0049
0.386
7.35
1.839
3.899
6.465
10.19
62.33
1.16
1015.53
7
64
ev07.0064
ev07_0064
0.328
7.67
2.154
5.093
8.503
12.30
99.08
1.06
1769.78
8
81
ev08.0081
ev08_0091
0.295
9.13
2.583
6.446
10.879
14.22
144.21
0.99
2884.36
9
100
ev09.0100
ev09_0100
0.271
10.03
2.959
7.958
14.020
16.40
198.06
0.88
4458.87
10
121
ev10.0121
ev10_0121
0.254
11.31
3.444
9.629
16.758
18.39
262.71
0.83
6599.29
11
144
ev11.0144
ev11_0144
0.228
12.03
3.857
11.459
20.164
20.68
335.96
0.78
9435.98
12
169
ev12.0169
ev12_0169
0.213
13.64
4.312
13.449
23.866
22.96
421.88
0.70
13092.24
13
196
ev13.0196
ev13_0196
0.198
13.74
4.698
15.597
28.569
25.51
516.77
0.67
17727.08
14
225
ev14.0225
ev14_0225
0.185
15.27
5.303
17.905
32.327
27.56
625.76
0.67
23485.82
15
256
ev15.0256
ev15_0256
0.177
16.74
5.699
20.372
37.338
30.25
742.40
0.64
30558.95
16
289
ev16.0289
ev16_0289
0.171
16.81
6.185
22.998
41.621
32.78
873.21
0.58
39107.62
17
324
ev17.0324
ev17_0324
0.158
18.15
6.610
25.783
48.017
35.55
1014.70
0.61
49344.21
18
361
ev18.0361
ev18_0361
0.150
18.85
7.131
28.727
56.061
38.13
1168.00
0.55
61470.41
19
400
ev19.0400
ev19_0400
0.146
19.64
7.846
31.831
61.146
40.28
1337.02
0.51
75681.47
20
441
ev20.0441
ev20_441
0.137
19.73
7.846
35.094
65.737
43.56
1515.94
0.52
92248.09
21
484
ev21.0484
ev21_0484
0.135
22.19
8.846
38.515
77.583
45.91
1708.64
0.46
111387.92
22
529
ev22.0529
ev22_0529
0.130
22.69
9.228
42.096
78.808
49.12
1908.16
0.49
133388.92
23
576
ev23.0576
ev23_0576
0.124
24.45
10.003
45.837
84.954
51.38
2131.90
0.44
158440.50
24
625
ev24.0625
ev24_0625
0.118
24.45
10.484
49.736
95.766
54.45
2362.85
0.43
186894.01
25
676
ev25.0676
ev25_0676
0.113
26.02
10.573
53.794
104.129
58.65
2608.32
0.43
219016.55
26
729
ev26.0729
ev26_0729
0.106
26.22
10.566
58.012
110.378
63.26
2866.48
0.45
255115.72
27
784
ev27.0784
ev27_0784
0.106
27.36
11.597
62.389
116.106
64.94
3140.56
0.41
295488.56
28
841
ev28.0841
ev28_0841
0.100
28.97
11.720
66.925
131.147
69.30
3423.27
0.44
340509.50
29
900
ev29.0900
ev29_0900
0.097
29.94
13.559
71.620
136.152
68.95
3730.28
0.36
390446.16


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