Table 4:

Convergence behavior of the averaging algorithm on (Sym⁺(3),g_can), initialized at the Frobenius mean, for the simulated data and actual DTI data. n = 6 for the DTI control group and dyslexia group, as described in Section 6. D is the radius of the smallest ball, centered at the Frobenius mean, containing all the data, and κ = κ(D) is as defined in Section 4.3. “Actual iterations needed” is the number of iterations that were needed for convergence with a canonical-distance threshold of 10⁻⁶. N_it(κ) is the smallest integer N for which κ^ND ≤ 10⁻⁶; see inequality (4.9).

n	m	D	κ	Actual Iterations Needed	Nit(κ)
6	6	2.1868	1.3965	8	N/A
6	24	0.8116	1.2106	4	N/A
6	48	0.5906	0.3481	4	13
6	96	0.3449	0.0854	3	5
6	192	0.3103	0.0680	3	5
6	288	0.2496	0.0431	3	4
18	6	3.1204	1.4751	8	N/A
18	24	1.1137	1.2628	5	N/A
18	48	0.6343	1.1751	5	N/A
18	96	0.4836	0.1866	4	8
18	192	0.3804	0.1060	4	6
18	288	0.3788	0.1049	4	6
36	6	3.7187	1.5147	9	N/A
36	24	1.2048	1.2769	5	N/A
36	48	0.8856	1.2242	4	N/A
36	96	0.5403	0.2529	3	10
36	192	0.4632	0.1676	3	7
36	288	0.2646	0.0486	3	4
Control Group		0.4346	0.1437	3	7
Dyslexia Group		0.3063	0.0662	3	5