Table 5:

CPU times (seconds) and optima for approximating the Horn variational index of a Horn matrix. Here n is the size of Horn matrix, PD is the proximal distance algorithm, aPD is the accelerated proximal distance algorithm, and Mosek is the Mosek solver.

Dimension	Optima			CPU Seconds
n	PD	aPD	Mosek	PD	aPD	Mosek
4	0.000000	0.000000	feasible	0.5555	0.0124	2.7744
5	0.000000	0.000000	infeasible	0.0039	0.0086	0.0276
8	0.000021	0.000000	feasible	0.0059	0.0083	0.0050
9	0.000045	0.000000	infeasible	0.0055	0.0072	0.0082
16	0.000377	0.000001	feasible	0.0204	0.0237	0.0185
17	0.000441	0.000001	infeasible	0.0204	0.0378	0.0175
32	0.001610	0.000007	feasible	0.0288	0.0288	0.1211
33	0.002357	0.000009	infeasible	0.0242	0.0346	0.1294
64	0.054195	0.000026	feasible	0.0415	0.0494	3.6284
65	0.006985	0.000026	infeasible	0.0431	0.0551	2.7862