Abstract
We develop methods for computing verified solutions of Sylvester matrix equations AX + XB = C . To this purpose we propose a variant of the Krawczyk interval operator with a factorized preconditioner so that the complexity is reduced to cubic when A and B are dense and diagonalizable. Block diagonalizations can be used in cases where A or B are not diagonalizable. The Lyapunov equation, as a special case, is also considered.
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