On the perturbation analysis of the maximal solution for the matrix equation $$ X-\overset{m}{\sum \limits_{i=1}}{A}_i^{\ast}\kern0.1em {X}^{-1}\kern0.1em {A}_i+\sum \limits_{j=1}^n{B}_j^{\ast}\kern0.1em {X}^{-1}\kern0.1em {B}_j=I $$

Journal of the Egyptian Mathematical Society

Table 1 Numerical results for the different values of k.

The perturbation bounds	Value of k
The perturbation bounds	2	3	4	5	6
$ \frac{\left\Vert\;{\tilde{X}}_L-{X}_L\right\Vert }{\left\Vert \kern0.24em {X}_L\right\Vert } $	1.1307 × 10⁻²	1.2043 × 10⁻³	1.2116 × 10⁻⁴	1.2123 × 10⁻⁵	1.2124 × 10⁻⁶
$ \frac{S_{err}}{\left\Vert \kern0.24em {X}_L\right\Vert } $	4.6564 × 10⁻²	3.9301 × 10⁻³	3.863 × 10⁻⁴	3.8564 × 10⁻⁵	3.8557 × 10⁻⁶

The perturbation bounds	Value of k
The perturbation bounds	2	3	4	5	6
\( \frac{\left\Vert\;{\tilde{X}}_L-{X}_L\right\Vert }{\left\Vert \kern0.24em {X}_L\right\Vert } \)	1.1307 × 10⁻²	1.2043 × 10⁻³	1.2116 × 10⁻⁴	1.2123 × 10⁻⁵	1.2124 × 10⁻⁶
\( \frac{S_{err}}{\left\Vert \kern0.24em {X}_L\right\Vert } \)	4.6564 × 10⁻²	3.9301 × 10⁻³	3.863 × 10⁻⁴	3.8564 × 10⁻⁵	3.8557 × 10⁻⁶