The sensitivity of the solution X to the matrix equation $AX - XB = C$ is primarily dependent on the quantity sep(A,B) introduced by Stewart (1973) in connection with the resolution of invariant subspaces. In this paper, we discuss some properties of 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.
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J. M. Varah (1979) studied this question.
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