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Lyapunov equation
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==Computational aspects of solution== The Lyapunov equation is linear; therefore, if <math>X</math> contains <math>n</math> entries, the equation can be solved in <math>\mathcal O(n^3)</math> time using standard matrix factorization methods. However, specialized algorithms are available which can yield solutions much quicker owing to the specific structure of the Lyapunov equation. For the discrete case, the Schur method of Kitagawa is often used.<ref>{{cite journal |last=Kitagawa |first=G. |title=An Algorithm for Solving the Matrix Equation X = F X F' + S |journal=International Journal of Control |volume=25 |issue=5 |pages=745–753 |year=1977 |doi=10.1080/00207177708922266 }}</ref> For the continuous Lyapunov equation the [[Bartels–Stewart algorithm]] can be used.<ref>{{cite journal |first=R. H. |last=Bartels |first2=G. W. |last2=Stewart |title=Algorithm 432: Solution of the matrix equation AX + XB = C |journal=Comm. ACM |volume=15 |year=1972 |issue=9 |pages=820–826 |doi=10.1145/361573.361582 |doi-access=free }}</ref>
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