Table 1 Error analysis for Example 4.1
From: On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)
s | \(\boldsymbol{\epsilon(X_{s})}\) | \(\boldsymbol{R_{1}(X_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Y_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{1,s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{2,s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(Z_{3,s})}\) |
|---|---|---|---|---|---|---|
0 | 3.90209 × 10−2 | 3.33430 × 10−2 | −3.82258 × 10−2 | 0.989301 | 0.980411 | 0.985409 |
1 | 5.67787 × 10−3 | 4.70245 × 10−3 | 1.11022 × 10−16 | 0.849272 | 0.807341 | 0.879195 |
2 | 9.75412 × 10−4 | 8.02922 × 10−4 | 4.48982 × 10−4 | 0.829614 | 0.783528 | 0.863646 |
3 | 1.72490 × 10−4 | 1.41756 × 10−4 | 4.83255 × 10−4 | 0.826170 | 0.779373 | 0.860915 |
4 | 3.07337 × 10−5 | 2.52483 × 10−5 | 4.87548 × 10−4 | 0.825560 | 0.778638 | 0.860431 |
5 | 5.48539 × 10−6 | 4.50591 × 10−6 | 4.88236 × 10−4 | 0.825451 | 0.778506 | 0.860345 |
6 | 9.79481 × 10−7 | 8.04563 × 10−7 | 4.88356 × 10−4 | 0.825431 | 0.778483 | 0.860329 |
7 | 1.74918 × 10−7 | 1.43680 × 10−7 | 4.88377 × 10−4 | 0.825428 | 0.778479 | 0.860327 |
8 | 3.12382 × 10−8 | 2.56594 × 10−8 | 4.88381 × 10−4 | 0.825427 | 0.778478 | 0.860326 |