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| Matrix Exponential http://forum.alglib.net/viewtopic.php?f=2&t=36 |
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| Author: | Leo [ Mon Jul 05, 2010 11:38 am ] |
| Post subject: | Matrix Exponential |
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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| Author: | Sergey.Bochkanov [ Mon Jul 05, 2010 2:06 pm ] |
| Post subject: | Re: Matrix Exponential |
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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| Author: | Leo [ Thu Jul 08, 2010 9:15 pm ] |
| Post subject: | Re: Matrix Exponential |
Thanks for the information. If you implement it in alglib, it will be great. |
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