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 Post subject: Cholesky decomposition with semi-positive definite matrices
PostPosted: Mon Aug 02, 2010 10:42 am 
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Joined: Mon Aug 02, 2010 10:15 am
Posts: 2
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


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 Post subject: Re: Cholesky decomposition with semi-positive definite matri
PostPosted: Tue Aug 03, 2010 9:32 pm 
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Joined: Fri May 07, 2010 7:06 am
Posts: 903
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.


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 Post subject: Re: Cholesky decomposition with semi-positive definite matri
PostPosted: Wed Aug 04, 2010 8:36 am 
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Joined: Mon Aug 02, 2010 10:15 am
Posts: 2
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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