A Bound on the Solution to a Structured Sylvester Equation with an Application to Relative Perturbation Theory

Assuming only that the spectra of A and B are disjoint as opposed to the more restrictive assumption previously used, we obtain a bound in all unitarily invariant norms on the solution to the structured Sylvester equation AX - XB = A1/2EB1/2. This bound is the first of its kind in all unitarily invariant norms under only the disjointedness assumption. An application of the bound to the relative perturbation theory for scaled Hermitian eigenvalue problems is given.

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