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Thread Subject:
cholesky factorization of a sparse,symmetric but not positive definite matrix

Subject: cholesky factorization of a sparse,symmetric but not positive definite matrix

From: kumar vishwajeet

Date: 8 Nov, 2010 17:23:04

Message: 1 of 3

Hi,
 Is there any method to find the cholesky factorization of a square,symmetric,sparse matrix which is not positive definite??
I am trying to find the cholesky factorization of:
5 0 0 0 0 0;
0 5 0 0 0 0
0 0 0 0 0 0
0 0 0 1 0 0
0 0 0 0 0 0
0 0 0 0 0 1]

Subject: cholesky factorization of a sparse,symmetric but not positive definite matrix

From: Bruno Luong

Date: 8 Nov, 2010 17:30:18

Message: 2 of 3

"kumar vishwajeet" <kwzeet@gmail.com> wrote in message <ib9blo$rmk$1@fred.mathworks.com>...
> Hi,
> Is there any method to find the cholesky factorization of a square,symmetric,sparse matrix which is not positive definite??

No, Cholesky is only defined for sdp matrix.

You light look at LDL factorization.

Bruno

Subject: cholesky factorization of a sparse,symmetric but not positive definite matrix

From: kumar vishwajeet

Date: 8 Nov, 2010 17:58:04

Message: 3 of 3

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <ib9c3a$op7$1@fred.mathworks.com>...
> "kumar vishwajeet" <kwzeet@gmail.com> wrote in message <ib9blo$rmk$1@fred.mathworks.com>...
> > Hi,
> > Is there any method to find the cholesky factorization of a square,symmetric,sparse matrix which is not positive definite??
>
> No, Cholesky is only defined for sdp matrix.
>
> You light look at LDL factorization.
>
> Bruno

That means there is no way to find the vector out of decomposition of a non-positive definite matrix. LDL will give me a matrix and I want a vector.

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