Minimum Norm (MN)
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 a quadrature rule.

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

Minimum Norm (MN) points

dn
Points
Images
(JPEG)
h
||Ln||
lmin
lavg
lmax
R
log det G
 || G-1 ||1
PE
1
4
mn01.0004
mn01_0004
1.231
2.00
0.318
0.318
0.318
2.00
-4.58
3.14
3.67
2
9
mn02.0009
 mn02_0009
0.848
3.06
0.387
0.716
0.978
4.08
-3.28
2.72
25.81
3
16
mn03.0016
mn03_0016
0.595
3.56
0.824
1.273
2.278
4.97
3.16
1.68
93.30
4
25
mn04.0025
mn04_0025
0.500
4.53
0.856
1.989
3.293
7.62
15.57
2.02
244.66
5
36
mn05.0036
mn05_0036
0.417
5.23
1.175
2.865
4.704
9.37
35.30
1.46
530.67
6
49
mn06.0049
mn06_0049
0.366
6.13
1.453
3.899
6.825
11.47
62.90
1.39
1013.88
7
64
mn07.0064
mn07_0064
0.305
6.59
1.610
5.093
8.734
14.23
99.61
1.11
1768.66
8
81
mn08.0081
mn08_0091
0.285
7.45
1.869
6.446
11.974
16.71
144.39
1.18
2883.49
9
100
mn09.0100
mn09_0100
0.253
8.18
2.112
7.958
14.658
19.41
198.70
1.02
4456.38
10
121
mn10.0121
mn10_0121
0.231
8.85
2.367
9.629
16.732
22.19
263.29
0.99
6596.97
11
144
mn11.0144
mn11_0144
0.218
9.61
2.768
11.459
20.790
24.42
336.69
0.94
9432.25
12
169
mn12.0169
mn12_0169
0.204
10.28
3.165
13.449
24.547
26.80
422.53
0.90
13089.52
13
196
mn13.0196
mn13_0196
0.187
11.03
3.261
15.597
28.372
30.62
517.91
0.79
17721.80
14
225
mn14.0225
mn14_0225
0.175
11.50
3.758
17.905
36.122
32.74
625.04
0.80
23487.52
15
256
mn15.0256
mn15_0256
0.171
12.35
3.995
20.372
38.235
36.13
742.62
0.77
30556.77
16
289
mn16.0289
mn16_0289
0.162
13.03
4.340
22.998
43.546
39.14
873.29
0.70
39106.40
17
324
mn17.0324
mn17_0324
0.153
13.74
4.956
25.783
48.430
41.06
1014.45
0.66
49343.55
18
361
mn18.0361
mn18_0361
0.146
14.34
5.271
28.727
59.656
44.36
1168.69
0.66
61464.40
19
400
mn19.0400
mn19_0400
0.140
14.98
5.659
31.831
68.212
47.43
1336.59
0.65
75681.95
20
441
mn20.0441
mn20_441
0.134
15.78
6.263
35.094
69.421
49.71
1515.63
0.58
92247.84
21
484
mn21.0484
mn21_0484
0.126
16.25
6.562
38.515
76.785
53.30
1707.49
0.57
111390.87
22
529
mn22.0529
mn22_0529
0.123
17.08
6.867
42.096
84.207
56.95
1910.64
0.54
133375.90
23
576
mn23.0576
mn23_0576
0.115
17.62
7.323
45.837
87.444
60.04
2130.63
0.52
158445.65
24
625
mn24.0625
mn24_0625
0.113
18.50
7.566
49.736
106.450
64.10
2361.57
0.51
186900.99
25
676
mn25.0676
mn25_0676
0.106
18.72
7.625
53.794
103.278
69.06
2609.39
0.51
219008.22
26
729
mn26.0729
mn26_0729
0.107
19.73
7.420
58.012
118.271
75.49
2865.61
0.55
255117.11
27
784
mn27.0784
mn27_0784
0.098
20.42
8.780
62.389
121.424
74.64
3140.42
0.47
295485.89
28
841
mn28.0841
mn28_0841
0.095
21.12
8.223
66.925
136.240
82.73
3422.25
0.56
340509.80
29
900
mn29.0900
mn29_0900
0.094
21.40
9.307
71.620
145.349
83.22
3726.27
0.47
390468.32


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