Table 6 Comparison results of the bounds for largest singular values of Example 2: the bold face numbers confirm our sharp perturbation bounds
From: Rank-one perturbation bounds for singular values of arbitrary matrices
| Â | Â | n | ||
|---|---|---|---|---|
20 | 40 | 60 | ||
Lower bounds | \(\sigma _{2}(A)\) | 16.18 | 40.04 | 32.54 |
\(Lb_{1}\) | 17.05 | 28.60 | 30.11 | |
\(Lb_{2}\) | 20.53 | 40.08 | 36.29 | |
Upper bounds | \(Ub_{1}\) | 46.13 | 68.25 | 70.57 |
\(Ub_{2}\) | 40.16 | 60.27 | 76.90 | |
\(\sigma _{1}(A)+\sigma _{1}(yx^{*})\) | 48.79 | 69.47 | 84.18 | |
Exact values | \(\sigma _{1}(A+yx^{*})\) | 27.57 | 53.13 | 49.27 |