Table 3 Error analysis for Example 4.3
From: On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)
s | \(\boldsymbol{\epsilon(X_{s})}\) | \(\boldsymbol{R_{1}(X_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Y_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{1,s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{2,s})}\) |
|---|---|---|---|---|---|
0 | 2.66052 × 10−1 | 1.56030 × 10−1 | −1.74299 × 10−1 | 0.900634 | 0.910937 |
4 | 1.95763 × 10−2 | 7.54210 × 10−3 | 1.94201 × 10−3 | 0.508120 | 0.455158 |
8 | 2.99945 × 10−3 | 1.09180 × 10−3 | 1.96189 × 10−3 | 0.483981 | 0.431403 |
12 | 4.96010 × 10−4 | 1.78894 × 10−4 | 1.96449 × 10−3 | 0.480380 | 0.427859 |
16 | 8.30170 × 10−5 | 2.98954 × 10−5 | 1.96492 × 10−3 | 0.479787 | 0.427276 |
20 | 1.39223 × 10−5 | 5.01230 × 10−6 | 1.96499 × 10−3 | 0.479688 | 0.427178 |
24 | 2.33562 × 10−6 | 8.40831 × 10−7 | 1.96500 × 10−3 | 0.479671 | 0.427162 |
28 | 3.91847 × 10−7 | 1.41065 × 10−7 | 1.96500 × 10−3 | 0.479669 | 0.427159 |
32 | 6.57408 × 10−8 | 2.36667 × 10−8 | 1.96500 × 10−3 | 0.479668 | 0.427158 |