Maximum Determinant (MD)
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 Determinant (MD) points

n
dn
Points
Images
(JPEG)
h
||Ln||
lmin
lavg
lmax
R
log det G
|| G-1 ||1
PE
1
4
md01.0004
md01_0004
1.231
2
0.318
0.318
0.318
2
-4.58
3.14
3.67
2
9
md02.0009
 md02_0009
0.818
3.24
0.463
0.716
0.895
3.73
-3.21
2.43
25.76
3
16
md03.0016
md03_0016
0.575
3.60
0.797
1.273
1.915
5.06
3.39
1.65
92.93
4
25
md04.0025
md04_0025
0.518
5.22
0.897
1.989
2.866
7.45
16.14
1.60
243.9
5
36
md05.0036
md05_0036
0.439
6.20
1.062
2.865
4.346
9.86
36.10
1.58
529.4
6
49
md06.0049
md06_0049
0.345
7.16
1.034
3.899
6.162
13.59
64.04
1.59
1011.9
7
64
md07.0064
md07_0064
0.308
8.19
1.353
5.093
8.388
15.52
100.69
1.16
1766.4
8
81
md08.0081
md08_0091
0.280
8.86
1.538
6.466
10.81
18.42
146.19
1.13
2879.6
9
100
md09.0100
md09_0100
0.236
9.61
1.788
7.958
13.59
21.10
201.56
1.04
4449.4
10
121
md10.0121
md10_0121
0.234
11.84
1.958
9.629
16.43
24.40
266.25
1.02
6588.6
11
144
md11.0144
md11_0144
0.224
14.05
1.733
11.459
20.09
30.86
341.40
1.08
9417.5
12
169
md12.0169
md12_0169
0.210
14.70
2.327
13.449
23.26
31.25
427.72
0.89
13072.4
13
196
md13.0196
md13_0196
0.181
15.16
2.045
15.597
27.61
38.67
524.38
1.02
17698.8
14
225
md14.0225
md14_0225
0.176
17.81
2.288
17.905
32.12
41.96
633.00
1.03
23455.4
15
256
md15.0256
md15_0256
0.161
18.08
2.321
20.372
36.69
47.40
753.03
1.04
30514.2
16
289
md16.0289
md16_0289
0.157
19.92
2.724
22.998
40.97
49.40
884.45
0.90
39058.9
17
324
md17.0324
md17_0324
0.147
21.55
2.562
25.783
45.96
57.10
1028.46
0.94
49279.6
18
361
md18.0361
md18_0361
0.140
21.08
3.073
28.727
52.078
58.09
1184.47
0.81
61386.8
19
400
md19.0400
md19_0400
0.132
23.64
2.973
31.831
58.300
65.44
1353.01
0.86
75599.8
20
441
md20.0441
md20_441
0.125
24.66
2.924
35.094
63.669
72.76
1534.48
0.85
92145.3
21
484
md21.0484
md21_0484
0.120
23.83
3.597
38.515
70.130
71.99
1729.34
0.71
111270.8
22
529
md22.0529
md22_0529
0.114
25.25
3.460
42.096
76.522
80.23
1936.12
0.73
133229.9
23
576
md23.0576
md23_0576
0.112
28.70
3.211
45.837
83.703
90.68
2157.00
0.83
158285.6
24
625
md24.0625
md24_0625
0.103
28.41
3.324
49.736
91.704
96.70
2391.13
0.87
186712.4
25
676
md25.0676
md25_0676
0.101
31.15
3.631
53.794
98.977
100.07
2639.30
0.81
218816.3
26
729
md26.0729
md26_0729
0.095
31.21
3.430
58.012
106.770
111.04
2900.63
0.79
254891.4
27
784
md27.0784
md27_0784
0.095
32.31
4.007
62.389
114.840
110.49
3175.88
0.76
295250.6
28
841
md28.0841
md28_0841
0.092
33.92
3.283
66.925
125.928
130.94
3465.60
0.90
340219.9
29
900
md29.0900
md29_0900
0.089
36.98
4.033
71.620
132.464
136.41
3769.59
0.70
390148.2

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