Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I
We consider the perturbation analysis of the matrix equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I. Based on the matrix differentiation, we first give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the sharpness of the perturbation bound....
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/784620 |
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| _version_ | 1832554474246242304 |
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| author | Xue-Feng Duan Qing-Wen Wang |
| author_facet | Xue-Feng Duan Qing-Wen Wang |
| author_sort | Xue-Feng Duan |
| collection | DOAJ |
| description | We consider the perturbation analysis of the matrix equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I. Based on the matrix differentiation, we first give a precise perturbation bound
for the positive definite solution. A numerical example is presented to illustrate the sharpness
of the perturbation bound. |
| format | Article |
| id | doaj-art-03ec4fce8e7e42aeb960005ae76cf873 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-03ec4fce8e7e42aeb960005ae76cf8732025-02-03T05:51:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/784620784620Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=IXue-Feng Duan0Qing-Wen Wang1School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaWe consider the perturbation analysis of the matrix equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I. Based on the matrix differentiation, we first give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the sharpness of the perturbation bound.http://dx.doi.org/10.1155/2012/784620 |
| spellingShingle | Xue-Feng Duan Qing-Wen Wang Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I Journal of Applied Mathematics |
| title | Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I |
| title_full | Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I |
| title_fullStr | Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I |
| title_full_unstemmed | Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I |
| title_short | Perturbation Analysis for the Matrix Equation X−∑i=1mAi∗XAi+∑j=1nBj∗XBj=I |
| title_sort | perturbation analysis for the matrix equation x ∑i 1mai∗xai ∑j 1nbj∗xbj i |
| url | http://dx.doi.org/10.1155/2012/784620 |
| work_keys_str_mv | AT xuefengduan perturbationanalysisforthematrixequationxi1maixaij1nbjxbji AT qingwenwang perturbationanalysisforthematrixequationxi1maixaij1nbjxbji |