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Analysis shows existence of nonnegative solutions in quadratic matrix equations, suggesting effective methods for resolution.
Quadratic matrix equations arise in many fields of scientific computing and engineering applications. In this paper, we study a class of quadratic matrix equations. Firstly, we prove the existence of minimal nonnegative solution for this quadratic matrix equation under a certain condition. Then, we propose some numerical methods for solving it. Finally, convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.
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Guan et al. (2025) studied this question.
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