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 Post subject: Matrix Exponential
PostPosted: Mon Jul 05, 2010 11:38 am 
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Joined: Mon Jul 05, 2010 11:13 am
Posts: 3
First of all I want compliment you for the very useful math library. I mostly program in Delphi, which has a lack of good mathematical libraries and alglib comes very handy.
I now need to calculate matrix exponentials. From a bit of experimentation I found it to be trickier than it seems at first, as it is easy to get the result swamped by rounding errors.
Having a good method in alglib will be great. Also any advice on how it is best to calculate it myself will be welcome.

Thanks


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 Post subject: Re: Matrix Exponential
PostPosted: Mon Jul 05, 2010 2:06 pm 
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Joined: Fri May 07, 2010 7:06 am
Posts: 878
If you have symmetric/Hermitian matrix, I recommend you to use EVD-based approach. Just calculate exp() of its eigenvalues and multiply from the left/right on its eigenvectors. In the general case, however, it is really hard to calculate. EVD-based approach is no good because unsymmetric matrices may be non-diagonalizable.

I recommend you to look at http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf and http://www.mathnet.or.kr/mathnet/kms_tex/230.pdf Pade-based method seems good enough and relatively easy to implement. ABLAS unit, especially RMatrixGEMM, may be handy when you'll try to multiply matrices.

P.S. I've added matrix exponentials in my todo list. But I think that it will take somewhere between month or three to implement given another problems I working on now.

UPD: second link should be http://www.cs.cornell.edu/cv/ResearchPDF/19ways+.pdf


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 Post subject: Re: Matrix Exponential
PostPosted: Thu Jul 08, 2010 9:15 pm 
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Joined: Mon Jul 05, 2010 11:13 am
Posts: 3
Thanks for the information.
If you implement it in alglib, it will be great.


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