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== Alternative approaches ==
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 efficient, iterative algorithms can potentially perform better. These include projection-based methods, which use [[Krylov subspace method|Krylov subspace]] iterations, methods based on the [[Alternating direction implicit method|alternating direction implicit]] (ADI) iteration, and hybridizations that involve both projection and ADI.<ref>{{Cite journal|last=Simoncini|first=V.|s2cid=17271167|date=2016|title=Computational Methods for Linear Matrix Equations|journal=SIAM Review|language=en-US|volume=58|issue=3|pages=377–441|doi=10.1137/130912839|issn=0036-1445|hdl=11585/586011|hdl-access=free}}</ref> Iterative methods can also be used to directly construct [[Low-rank approximation|low rank approximations]] to <math>X</math> when solving <math>AX-XB = C</math>.
== References ==
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