TITLE:
Numerical Solution of the Quaternion Quadratic Matrix Equation X 2 +BX+C=0
AUTHORS:
Baiquan Hu
KEYWORDS:
Quadratic Matrix Equations, Quaternion Matrices, M-Matrices, Fixed-Point Iteration Method, Comparison Matrix
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
13,
2025
ABSTRACT: This paper addresses a class of numerical solution problems for quaternion quadratic matrix equations arising from practical engineering applications. By transforming it into a special Riccati equation, a sufficient condition for the existence of solutions to the corresponding M-matrix equation is derived using the theory of comparison matrices. This condition is then applied to investigate the existence of solutions for the quaternion quadratic matrix equation. Finally, numerical examples demonstrate an effective solution method for the quaternion quadratic matrix equation using fixed-point iteration.