Numerical solutions of Quaternionic Riccati equations

Inspired by the study of complex nonsymmetric algebraic Riccati equations, we investigate nonsymmetric algebraic Riccati equations for quaternionic matrices. We introduce the comparison matrix of a quaternionic matrix, extending that of a complex matrix, and use it to give a condition for the existence and uniqueness of the extremal solution. The solution can be obtained by a fixed-point iteration.