Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt
https://doi.org/10.1186/s42787-019-0052-7
Abstract
In this paper, we study the perturbation estimate of the maximal solution for the matrix equation X− X i¼1 m A i X−1 Ai þXn j¼1 B j X−1 Bj ¼ I using the differentiation of matrices. We derive the differential bound for this maximal solution. Moreover, we present a perturbation estimate and an error bound for this maximal solution. Finally, a numerical example is given to clarify the reliability of our obtained results.
Ramadan, M., & El–Shazly, N. (2020). On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I. Journal of the Egyptian Mathematical Society, 28(1), 1-13. doi: https://doi.org/10.1186/s42787-019-0052-7
MLA
Mohamed A. Ramadan; Naglaa M. El–Shazly. "On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I", Journal of the Egyptian Mathematical Society, 28, 1, 2020, 1-13. doi: https://doi.org/10.1186/s42787-019-0052-7
HARVARD
Ramadan, M., El–Shazly, N. (2020). 'On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I', Journal of the Egyptian Mathematical Society, 28(1), pp. 1-13. doi: https://doi.org/10.1186/s42787-019-0052-7
VANCOUVER
Ramadan, M., El–Shazly, N. On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I. Journal of the Egyptian Mathematical Society, 2020; 28(1): 1-13. doi: https://doi.org/10.1186/s42787-019-0052-7
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