Numerical algorithm for solving quadratic matrix equations of a certain class

摘要

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 x n matrices, and the neutral subspaces of the 2n x 2n matrix . 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.