Table 2 Error analysis for Example 4.2
From: On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)
s | \(\boldsymbol{\epsilon(X_{s})}\) | \(\boldsymbol{R_{1}(X_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Y_{s})}\) | \(\boldsymbol{\lambda} _{\mathbf{min}}\boldsymbol{(Z_{1,s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{2,s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{3,s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{4,s})}\) |
|---|---|---|---|---|---|---|---|
0 | 4.81432 × 10−2 | 3.79180 × 10−2 | −4.33175 × 10−2 | 0.984520 | 0.982228 | 0.984476 | 0.987805 |
1 | 1.02252 × 10−2 | 7.49107 × 10−3 | −1.78032 × 10−18 | 0.719649 | 0.902084 | 0.604645 | 0.831201 |
2 | 2.73413 × 10−3 | 2.08835 × 10−3 | 1.05313 × 10−3 | 0.664911 | 0.883407 | 0.535912 | 0.795502 |
3 | 6.45772 × 10−4 | 5.05650 × 10−4 | 1.33072 × 10−3 | 0.652517 | 0.879228 | 0.521034 | 0.787317 |
4 | 1.40122 × 10−4 | 1.08374 × 10−4 | 1.41687 × 10−3 | 0.650050 | 0.878406 | 0.518114 | 0.785684 |
5 | 3.17484 × 10−5 | 2.37848 × 10−5 | 1.43915 × 10−3 | 0.649533 | 0.878227 | 0.517495 | 0.785339 |
6 | 7.96360 × 10−6 | 5.93391 × 10−6 | 1.44386 × 10−3 | 0.649401 | 0.878180 | 0.517334 | 0.785250 |
7 | 2.02969 × 10−6 | 1.53853 × 10−6 | 1.44486 × 10−3 | 0.649366 | 0.878167 | 0.517291 | 0.785226 |
8 | 4.91154 × 10−7 | 3.76520 × 10−7 | 1.44510 × 10−3 | 0.649357 | 0.878164 | 0.517280 | 0.785220 |
9 | 1.14634 × 10−7 | 8.75007 × 10−8 | 1.44517 × 10−3 | 0.649355 | 0.878164 | 0.517278 | 0.785219 |
10 | 2.71333 × 10−8 | 2.05092 × 10−8 | 1.44518 × 10−3 | 0.649354 | 0.878164 | 0.517277 | 0.785219 |