In[]:=
Sat 18 Nov 2023 15:15:48
Parent notebook: https://www.wolframcloud.com/obj/yaroslavvb/newton/lyapunov.nb
Forum q: https://math.stackexchange.com/questions/4808422/least-squares-solution-to-underdetermined-lyapunov-equation
Forum q: https://math.stackexchange.com/questions/4808422/least-squares-solution-to-underdetermined-lyapunov-equation
Init
Init
Main
Main
In[]:=
d=3;SeedRandom[1];ii=IdentityMatrix[d];{A,B}=RandomInteger[{-2,2},{2,d,d}];A=makePosdef[A];B=makePosdef[B];Print["A=",A//MatrixForm];Print["B=",B//MatrixForm];sol1=lyapLeastSquares[A,B];sol2=lyapSpectral[A,B];Print["solution least squares: ",sol1//MatrixForm];Print["solution lyapunov: ",sol2//Simplify//MatrixForm];
A=
8 | -8 | -8 |
-8 | 9 | 8 |
-8 | 8 | 8 |
B=
5 | 5 | -5 |
5 | 9 | -3 |
-5 | -3 | 6 |
errorLsqr=
1
4
errorSpectral=0.25
solution least squares:
1789 640 | 183 40 | - 1329 640 |
183 40 | 73 10 | - 123 40 |
- 1329 640 | - 123 40 | 869 640 |
solution lyapunov:
1789 640 | 183 40 | - 1329 640 |
183 40 | 73 10 | - 123 40 |
- 1329 640 | - 123 40 | 869 640 |