In this paper we investigate the nonlinear matrix equation X + A T √ X −1 A = P, for the existence of positive definite solutions. Bounds for X −1L and X −1 are derived where X L is the maximal solution and X is any other positive definite solution of this matrix equation. A perturbation estimate for the maximal solution and an error bound for approximate solutions are derived. A numerical example is given to illustrate the reliability of the obtained results.
El-Shazly, N. (2016). On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P. Journal of the Egyptian Mathematical Society, 24(4), 644-649. doi: 10.1016/j.joems.2016.04.004
MLA
Naglaa M. El-Shazly. "On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P", Journal of the Egyptian Mathematical Society, 24, 4, 2016, 644-649. doi: 10.1016/j.joems.2016.04.004
HARVARD
El-Shazly, N. (2016). 'On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P', Journal of the Egyptian Mathematical Society, 24(4), pp. 644-649. doi: 10.1016/j.joems.2016.04.004
VANCOUVER
El-Shazly, N. On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P. Journal of the Egyptian Mathematical Society, 2016; 24(4): 644-649. doi: 10.1016/j.joems.2016.04.004
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