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| Solutions to Lyapunov matrix equation http://forum.alglib.net/viewtopic.php?f=2&t=631 |
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| Author: | chi [ Fri Oct 19, 2012 5:17 pm ] |
| Post subject: | Solutions to Lyapunov matrix equation |
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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| Author: | Sergey.Bochkanov [ Sun Oct 21, 2012 6:59 pm ] |
| Post subject: | Re: Solutions to Lyapunov matrix equation |
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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| Author: | chi [ Tue Oct 30, 2012 4:10 pm ] |
| Post subject: | Re: Solutions to Lyapunov matrix equation |
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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