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
Ran, A.C.M., Reurings, M.C.B.: On the nonlinear matrix equation X + A * F(X)A = Q solutions and perturbation theory. J. Linear Algebra Appl. 372, 33–51 (2002)
Zhang, Y.: On Hermitian Positive definite solutions of the matrix equation. J. Linear Algebra Appl. 372, 295–304 (2003)
EL-say, S.M., AI-Dbiban, A.M.: On Positive definite solutions of a matrix equationX + A * X − n A = I. J. Appl. Math. Comput. 151, 533–541 (2004)
Hasanov, V.I.: Positive definite solutions of the matrix equation. J. Linear Algebra Appl. 404, 166–182 (2005)
Hasanov, V.I., Ivanov, I.G.: Solutions and perturbation estimates for the matrix equation X±A * X − n A = Q. J. Applied Mathematics and Computation 156, 513–525 (2004)
Bharia, R.: Matrix analysis. Springer, Berlin (1997)
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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
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