On the Separation of Two Matrices
J. M. Varah · SIAM Journal on Numerical Analysis · 1979
The sensitivity of the solution X to the matrix equation $AX - XB = C$ is primarily dependent on the quantity ${\operatorname{sep}}(A,B)$ introduced by Stewart (1973) in connection with the resolution of invariant subspaces. In this paper, we discuss some properties of ${\operatorname{sep}}(A,B)$, give some examples to show how very small it can be for seemingly harmless problems, and discuss the feasibility of the iteration $AX^{(k + 1)} = X^{(k)} B + C$ for solving the matrix equation.