Abstract
The nonlinear matrix equation \( X^{r} + \sum\nolimits_{i = 1}^{m} {A_{i}^{*} } X^{{\delta_{i} }} A_{i} = Q \) is studied. A necessary condition for the existence of positive definite solutions of this equation is derived. Based on the Banach fixed point theorem, a sufficient condition for the existence of a unique positive definite solution of this equation is also derived. Iterative methods for obtaining the extremal (maximal–minimal) positive definite solutions of this equation are proposed.
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Wang, B., Li, Q. (2013). On the Existence of Extremal Positive Definite Solutions of a Class of Nonlinear Matrix Equation. In: Yin, Z., Pan, L., Fang, X. (eds) Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013. Advances in Intelligent Systems and Computing, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37502-6_18
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DOI: https://doi.org/10.1007/978-3-642-37502-6_18
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