On Using the Shcur Method for Solving Unilateral Quadratic Matrix Equation

摘要

The algorithm of solving the unilateral quadratic matrix equation is proposed. The algorithm is based on the Cayley transform of a matrix pencil and Schur algorithm, which is commonly used to find the solution of the algebraic Riccati equation. This algorithm allows one to find solution in the case of a singular matrix as well which is a coefficient of the higher degree of the equation. As shown in the example, the proposed algorithm is also effective in the case where all the matrix coefficients of this equation are degenerate. The algorithm efficiency is demonstrated in the examples that other authors have examined.