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Cholesky decomposition with semi-positive definite matrices http://forum.alglib.net/viewtopic.php?f=2&t=47 |
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Author: | hayt [ Mon Aug 02, 2010 10:42 am ] |
Post subject: | Cholesky decomposition with semi-positive definite matrices |
Hello, I am using the c++ alglib 2.6 to calculate the cholesky decomposition and call the hpdmatrixcholesky-function which always returns false on a spd(semi positive definte) matrix. (like 4x4 all filled with 1) Now I read in the header that the library returns false on not positive finite matrices. But my math understanding (and wikipedia ^^) tells me you only need spd matrices. Is this only a wrong formulation is the header or is this a bug and cholesky does not work with spd-matrices? Greetz Ricardo |
Author: | Sergey.Bochkanov [ Tue Aug 03, 2010 9:32 pm ] |
Post subject: | Re: Cholesky decomposition with semi-positive definite matri |
It work with strictly positive definite matrices only. Semidefinite matrices are not supported. Can you explain in more details what is wrong with header? I don't get it :) it talks about positive definite matrices; it is well known that Cholesky decomposition is stable only for strictly positive definite matrices. |
Author: | hayt [ Wed Aug 04, 2010 8:36 am ] |
Post subject: | Re: Cholesky decomposition with semi-positive definite matri |
Ah sorry you are right of course. I just remembered that you can use the cholesky decomposition for semi-positive definite matrices, but I forgot that there is no stable computation for those. The explanation in the header is correct in that case, too. So I think this thread can be closed. Thx for your time :) Ricardo |
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