Numerical algorithm for solving quadratic matrix equations of a certain class
Yu. O. Vorontsov, Х. Д. Икрамов · Computational Mathematics and Mathematical Physics · 2014
A relationship is found between the solutions to the quadratic matrix equation X T DX + AX + X T B + C = 0, where all the matrix coefficients are n × n matrices, and the neutral subspaces of the 2n × 2n matrix $M = \left( \begin{gathered} CA \hfill \\ BD \hfill \\ \end{gathered} \right) $ . This relationship is used to design an algorithm for solving matrix equations of the indicated type. Numerical results obtained with the help of the proposed algorithm are presented.