Table 4 Error analysis for Example 4.4
From: On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)
s | \(\boldsymbol{\epsilon(X_{s})}\) | \(\boldsymbol{R_{2}(X_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(I+\sum_{i=1}^{4}A_{i}^{*}A_{i}-X_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(X_{s}-I)}\) |
|---|---|---|---|---|
0 | 8.55046 × 10−1 | 2.65 | 0.715946 | 0 |
10 | 1.83959 × 10−1 | 3.26477 × 10−1 | 0.544118 | 0.076489 |
20 | 1.06950 × 10−2 | 1.87085 × 10−2 | 0.493691 | 0.098958 |
30 | 5.94976 × 10−4 | 1.04066 × 10−3 | 0.490594 | 0.100375 |
40 | 3.30916 × 10−5 | 5.78794 × 10−5 | 0.490422 | 0.100455 |
50 | 1.84048 × 10−6 | 3.21913 × 10−6 | 0.490412 | 0.100459 |
60 | 1.02364 × 10−7 | 1.79042 × 10−7 | 0.490411 | 0.100459 |
70 | 5.69327 × 10−9 | 9.95792 × 10−9 | 0.490411 | 0.100459 |