Bartels-Stewart Algorithm

In numerical linear algebra, the Bartels-Stewart algorithm is used to numerically solve the Sylvester matrix equation. Developed by R. H. Bartels and G. W. Stewart in 1971, it was the first numerically stable method that could be systematically applied to such equations, transforming the equation into a triangular system by using the real Schur decompositions of its matrices, then solving that system by forward or backward substitution. In 1979 G. Golub, C. Van Loan and S. Nash introduced an improved version known as the Hessenberg-Schur algorithm, but the original method remains a standard approach for solving Sylvester equations of small to moderate size. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/