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Table 5 Error analysis for Example 4.5

From: On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)

s

\(\boldsymbol{\epsilon(X_{s})}\)

\(\boldsymbol{R_{2}(X_{s})}\)

\(\boldsymbol{\lambda}_{\mathbf{min}}\boldsymbol{(I+\sum_{i=1}^{3}A_{i}^{*}A_{i}-X_{s})}\)

\(\boldsymbol{\lambda} _{\mathbf{min}}\boldsymbol{(X_{s}-I)}\)

0

2.10332 × 10−1

2.95400 × 10−1

0.047059

0

3

3.11244 × 10−2

4.52684 × 10−2

0.017503

0.028153

6

5.17330 × 10−3

8.36352 × 10−3

0.023078

0.023109

9

1.10730 × 10−3

1.75717 × 10−3

0.022155

0.023907

12

2.28175 × 10−4

3.63481 × 10−4

0.022341

0.023751

15

4.73953 × 10−5

7.54424 × 10−5

0.022303

0.023783

18

9.83002 × 10−6

1.56497 × 10−5

0.022311

0.023776

21

2.03950 × 10−6

3.24685 × 10−6

0.022309

0.023778

24

4.23122 × 10−7

6.73607 × 10−7

0.022310

0.023777

27

8.77834 × 10−8

1.39750 × 10−7

0.022310

0.023777

30

1.82120 × 10−8

2.89934 × 10−8

0.022310

0.023777