Bartels–Stewart algorithm: Difference between revisions

Revision as of 20:24, 20 September 2018

Revision as of 20:48, 20 September 2018

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== Implementations and availability ==

== Alternative approaches and related problems ==

For large systems, the <math>\mathcal{O}(m^3 + n^3)</math>cost of the Bartels-Stewart algorithm can be prohibitive. When <math>A</math>and <math>B</math> are sparse or structured, so that linear solves and matrix vector multiplies involving them are cheap, iterative algorithms can potentially perform better. These include projection-based methods, which use Krylov subspace iterations, methods based on the alternating-implicit direction (ADI) iteration, and hybridizations that involve both projection and ADI. Iterative methods can also be used to directly construct low rank approximations to <math>X</math> when solving <math>AX-XB = C</math>. This is important when, for instance, <math>X</math> is too large to be stored in memory explicitly.

== References ==