Article citationsMore>>

Higham, N.J. and Kim, H. (2001) Solving a Quadratic Matrix Equation by Newton’s Method with Exact Line Searches. SIAM Journal on Matrix Analysis and Applications, 23, 303-316.
https://doi.org/10.1137/s0895479899350976

has been cited by the following article:

• 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.