Numerical Solution of a Semilinear Matrix Equation of the Stein Type in the Normal Case

Abstract

It is known that the solution of the semilinear matrix equation X − AX*B = C can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. A technique for solving the original semilinear equation in the normal case is proposed. For equations of the order n = 3000, this allows us to cut the time of computation almost in half, compared toMatlab’s library function dlyap, which solves Stein equations in the Matlab package.