Table 2 Summary Results for Example 5 on Theorems 6 and 7
From: On solution and perturbation estimates for the nonlinear matrix equation \(X-A^{*}e^{X}A=I\)
h | 8 | 12 | 14 |
|---|---|---|---|
\(\theta\) | 0.941753527133053 | 0.941753527161009 | 0.941753527161012 |
\(\theta _{1}\) | 1.058246472866947 | 1.058246472838991 | 1.058246472838988 |
\(\triangle A\) | 3.803542495682596 \(\times 10^{-9}\) | 3.803542495682596 \(\times 10^{-13}\) | 3.803542495682595 \(\times 10^{-15}\) |
\(\triangle I\) | 4.757828150777915 \(\times 10^{-9}\) | 4.757828150777916 \(\times 10^{-13}\) | 4.757828150777915 \(\times 10^{-15}\) |
RE | 4.149368237008739 \(\times 10^{-9}\) | 4.148922653233927 \(\times 10^{-13}\) | 4.298515873338060 \(\times 10^{-15}\) |
C1 | 4.388248825247514 \(\times 10^{-9}\) | 4.386793311723082 \(\times 10^{-13}\) | 4.370373519357924 \(\times 10^{-15}\) |
C2 | 3.918479562381102\(\times 10^{-9}\) | 3.917179864079730 \(\times 10^{-13}\) | 3.902517837525337 \(\times 10^{-15}\) |
C3 | 6.186428071767561\(\times 10^{-8}\) | 6.186428071583923 \(\times 10^{-12}\) | 6.186428071583904 \(\times 10^{-14}\) |