A Stein equation approach for solutions to the Bezout identity and the generalized Bezout identity

This paper is concerned with the solutions to the Bezout identity and the generalized Bezout identity. Analytical solutions are obtained by solving a class of Stein equations with nilpotent coefficient matrices. As long as the Stein equations are solved by existing methods in a numerically stable way, all the elements of the Bezout identity and the generalized Bezout identity can be expressed explicitly. The problem of finding solutions to a class of generalized Sylvester equations is reconsidered to illustrate the application and efficiency of the proposed approach.