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Update doc/solvers/LyapunovSylvester.md
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doc/solvers/LyapunovSylvester.md

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@@ -58,12 +58,12 @@ controllability gramian $X = \sum_{k=0}^{\infty} A^k Q (A^\top)^k$.
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## Complexity Analysis
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| Case | Time | Space | Notes |
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|------------------------|--------------------|-----------------------------|---------------------------------------------|
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| $N{=}M{=}2$ | $O(64)$ flops | $O(NM)^2 = 16$ floats for K | 4×4 linear system |
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| $N{=}M{=}3$ | $O(729)$ flops | 81 floats for K | 9×9 linear system |
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| General $N{=}M$ | $O(N^6)$ flops | $O(N^4)$ words | Gaussian elimination on the $N^2 \times N^2$ Kronecker system |
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| Alternative (Bartels–Stewart) | $O(N^3)$ | $O(N^2)$ | Requires Schur decomposition; preferred for $N \geq 6$ |
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| Case | Time | Space | Notes |
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|-------------------------------|----------------|-----------------------------|---------------------------------------------------------------|
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| $N{=}M{=}2$ | $O(64)$ flops | $O(NM)^2 = 16$ floats for K | 4×4 linear system |
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| $N{=}M{=}3$ | $O(729)$ flops | 81 floats for K | 9×9 linear system |
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| General $N{=}M$ | $O(N^6)$ flops | $O(N^4)$ words | Gaussian elimination on the $N^2 \times N^2$ Kronecker system |
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| Alternative (Bartels–Stewart) | $O(N^3)$ | $O(N^2)$ | Requires Schur decomposition; preferred for $N \geq 6$ |
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For the embedded sizes ($N \leq 5$) targeted by this library the Kronecker approach is negligibly
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more expensive than Bartels–Stewart and avoids the full Schur machinery.

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