engleski

Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts

The solution to a general Sylvester equation AX− XB = GF* with a low rank righthand side is analyzed quantitatively through Low-rank Alternating-Directional- Implicit method (LR-ADI) with exact shifts. New bounds and perturbation bounds on X are obtained. A distinguished feature of these bounds is that they reflect the interplay between the eigenvalue decompositions of A and B and the right-hand side factors G and F. Numerical examples suggest that because of this inclusion of details, new perturbation bounds are much sharper than the existing ones.

Sylvester equation; Low-rank Alternating-Directional-Implicit (LR-ADI) method; Upper bounds; Perturbation bounds

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