Table 2 Comparison of the bounds in (10) for smallest singular values of Example 1: the bold face numbers confirm our sharp perturbation bounds
From: Rank-one perturbation bounds for singular values of arbitrary matrices
| Â | Â | n | ||
|---|---|---|---|---|
60 | 90 | 120 | ||
Lower bounds | \(Lb_{1}\) | 11.63 | 20.14 | 18.90 |
\(Lb_{2}\) | 12.76 | 20.62 | 14.23 | |
Upper bounds | \(\sigma _{n-1}(A)\) | 21.05 | 41.64 | 38.60 |
\(Ub_{1}\) | 20.83 | 39.83 | 34.53 | |
\(Ub_{2}\) | 24.47 | 43.08 | 33.64 | |
Exact values | \(\sigma _{n}(A+yx^{*})\) | 18.92 | 29.27 | 21.92 |