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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 \(\times 10^{-14}\)