The iterative solution of the matrix equation \(XA+BX+C=0\)
The paper deals with the linear matrix equation \(XA+BX+C=0\) in the unknown matrix X. The aim is to present a unified theory for the iterative solution of this equation. Two well known iterative algorithms, converging when A and B are stable, are realized as special cases of the proposed unified method. The convergence of the unified algorithm does not depend on the stability of A and B, but occurs whenever the matrix equation has a unique solution. Finally, a theoretical algorithm based on a matrix polynomial is presented; it requires the construction of characteristic or interpolating polynomials.
scientific article; zbMATH DE number 4084852