A Heuristic Method for Solving Polynomial Matrix Equations
We propose a heuristic method to solve polynomial matrix equations of the type ∑=1= , where are scalar coefficients and X and B are square matrices of order n. The method is based on the decomposition of the B matrix as a linear combination of the identity matrix and an idempotent, involutive, or ni...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Oviedo (UNIOVI) |
| Repositorio: | RUO. Repositorio Institucional de la Universidad de Oviedo |
| Idioma: | inglés |
| OAI Identifier: | oai:digibuo.uniovi.es:10651/72148 |
| Acceso en línea: | https://hdl.handle.net/10651/72148 https://dx.doi.org/10.3390/axioms13040239 |
| Access Level: | acceso abierto |
| Palabra clave: | polynomial matrix equations idempotent matrix involutive matrix nilpotent matrix |
| Sumario: | We propose a heuristic method to solve polynomial matrix equations of the type ∑=1= , where are scalar coefficients and X and B are square matrices of order n. The method is based on the decomposition of the B matrix as a linear combination of the identity matrix and an idempotent, involutive, or nilpotent matrix. We prove that this decomposition is always possible when =2. Moreover, in some cases we can compute solutions when we have an infinite number of them (singular solutions). This method has been coded in MATLAB and has been compared to other methods found in the existing literature, such as the diagonalization and the interpolation methods. It turns out that the proposed method is considerably faster than the latter methods. Furthermore, the proposed method can calculate solutions when diagonalization and interpolation methods fail or calculate singular solutions when these methods are not capable of doing so. |
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