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 Post subject: Solutions to Lyapunov matrix equation
PostPosted: Fri Oct 19, 2012 5:17 pm 
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Joined: Fri Oct 19, 2012 4:28 pm
Posts: 8
I am needing to implement the solution to the Lyapunov matrix equation: A*X + X*A' + B*B' = 0

Does algilib have a method for this already? If not will algilb have enough tools to implement the proper algorithm for solving this? Most people refer to the Bartels-Stewert algorithm (http://dl.acm.org/citation.cfm?id=361582) and MATLAB is based on that as well, but draws from SILCOT.

Any guidance on this would be helpful,

Thank you,


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 Post subject: Re: Solutions to Lyapunov matrix equation
PostPosted: Sun Oct 21, 2012 6:59 pm 
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Joined: Fri May 07, 2010 7:06 am
Posts: 878
No, ALGLIB has no ready solution for this problem. I haven't worked with such problems before and can't say anything on how they can be solved with ALGLIB.


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 Post subject: Re: Solutions to Lyapunov matrix equation
PostPosted: Tue Oct 30, 2012 4:10 pm 
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Joined: Fri Oct 19, 2012 4:28 pm
Posts: 8
No worries,

After some digging I found this paper: http://aero-comlab.stanford.edu/Papers/jameson_007.pdf
Which offers a solution to the problem that only involves finding eigenvalues, matrix inversions, and basic matrix operations, all of which ALGlib can do. My test algorithms in MATLAB based on this paper works well for my class of matrices. I am pretty confident it will do the trick, but I cannot say anything about its computational intensity over other solutions I ran across, like

http://dl.acm.org/citation.cfm?id=361582

which is an old paper with source code in fortran.


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