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Table 1 Summary of Results for Example 4 for different \(\delta\) with \(X_{0}=I\) and \(Z_{0}=0\)

From: On solution and perturbation estimates for the nonlinear matrix equation  \(X-A^{*}e^{X}A=I\)

\(\delta\) Iterations allowed Iterations performed residual = \(\Vert X-A^{*}e^{X}A-I\Vert _{F}\)
1 1000 Over 1000 3.36\(\times 10^{+02}\)
0.1 1000 Over 1000 5.32\(\times 10^{+00}\)
0.01 1000 Over 1000 8.37 \(\times 10^{-02}\)
0.001 1000 1 2.03 \(\times 10^{-12}\)