Table 6 Error analysis for Example 4.6
From: On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)
s | \(\boldsymbol{\epsilon(X_{s})}\) | \(\boldsymbol{R_{2}(X_{s})}\) | \(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(I+\sum_{i=1}^{2}A_{i}^{*}A_{i}-X_{s})}\) | \(\boldsymbol{\lambda} _{\mathbf{min}}\boldsymbol{(X_{s}-I)}\) |
|---|---|---|---|---|
0 | 8.94901 × 10−1 | 3.72279 | 0.501528 | 0 |
40 | 8.72900 × 10−2 | 1.79569 × 10−1 | 0.195273 | 0.120468 |
80 | 1.70413 × 10−2 | 3.36946 × 10−2 | 0.185914 | 0.131596 |
120 | 3.26922 × 10−3 | 6.41673 × 10−3 | 0.184203 | 0.133762 |
160 | 6.23654 × 10−4 | 1.22239 × 10−3 | 0.183879 | 0.134178 |
200 | 1.18834 × 10−4 | 2.32858 × 10−4 | 0.183817 | 0.134257 |
240 | 2.26383 × 10−5 | 4.43579 × 10−5 | 0.183805 | 0.134272 |
280 | 4.31248 × 10−6 | 8.44986 × 10−6 | 0.183803 | 0.134275 |
320 | 8.21498 × 10−7 | 1.60964 × 10−6 | 0.183803 | 0.134276 |
360 | 1.56490 × 10−7 | 3.06625 × 10−7 | 0.183803 | 0.134276 |
400 | 2.98101 × 10−8 | 5.84098 × 10−8 | 0.183803 | 0.134276 |