On the Theory of Nonlinear Matrix Equation X s  = Q + A H (I ⊗ X − C)− δ A

Liu, Wei; Sang, Haifeng; Li, Qingchun; Zhai, Chunwei

doi:10.1007/978-3-662-45049-9_45

Wei Liu¹⁶,
Haifeng Sang¹⁶,
Qingchun Li¹⁶ &
…
Chunwei Zhai¹⁶

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 472))

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Abstract

In this paper, the nonlinear matrix equation X ^s = Q±A ^H(I ⊗ X − C)^− δ A are discussed. We present some necessary and sufficient conditions for the existence of a definite positive solution for this equation, and some related properties of the definite positive solution such as boundary.

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References

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Authors and Affiliations

College of Mathematics and Statistics, Beihua University, Jilin, 132013, China
Wei Liu, Haifeng Sang, Qingchun Li & Chunwei Zhai

Authors

Wei Liu
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Haifeng Sang
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Qingchun Li
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Chunwei Zhai
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Editors and Affiliations

Huazhong University of Science and Technology, 430074, Wuhan, China
Linqiang Pan
Institute of Mathematics of the Romanian Academy, 014700, Bucuresti, Romania
Gheorghe Păun
Department of Computer Science and Artificial Intelligence, University of Sevilla, Avda. Reina Mercedes s/n., 41012, Sevilla, Spain
Mario J. Pérez-Jiménez
School of Automation, Huazhong University of Science and Technology, 430074, Wuhan, China
Tao Song

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Liu, W., Sang, H., Li, Q., Zhai, C. (2014). On the Theory of Nonlinear Matrix Equation X ^s = Q + A ^H(I ⊗ X − C)^− δ A . In: Pan, L., Păun, G., Pérez-Jiménez, M.J., Song, T. (eds) Bio-Inspired Computing - Theories and Applications. Communications in Computer and Information Science, vol 472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45049-9_45

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DOI: https://doi.org/10.1007/978-3-662-45049-9_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45048-2
Online ISBN: 978-3-662-45049-9
eBook Packages: Computer ScienceComputer Science (R0)

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On the Theory of Nonlinear Matrix Equation X s = Q + A H(I ⊗ X − C)− δ A