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## Re: sparse symmetric matrices

 From: David Bateman Subject: Re: sparse symmetric matrices Date: Sun, 12 Jun 2011 09:44:15 +0200 User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv:1.9.2.17) Gecko/20110516 Thunderbird/3.1.10

```On 06/11/2011 09:38 PM, Bill Greene wrote:
> I guess I should have mentioned that I did try:
>
> u = ks \ b'
>
> This returns an incorrect solution, u.
> I also tried to let chol() compute a permutation
> [lt, err, p] = chol(ks, 'vector');
> and this results in an incorrect solution, also.
>
> I'm guessing all of these errors are related: I'm
> creating only the upper triangle and, when permuted,
> entries end up in both triangles.
>
> I'm hoping someone has a good strategy for dealing with
> this.
>
> Bill
>

Because Octave is recognising that the matrix is upper triangular and
treating it as such, even though the choloesky only uses the upper
triangular part of the matrix. I only see one solution

Tell Octave that the matrix is positive definite rather than upper
triangular. cf

octave:1> n = 1000; d = 0.1; a = sprand(n,n,d); s0 = matrix_type(a *
a',"positive definite"); x = rand(n,1); y0 = s0 \ x; s1 =
matrix_type(triu(s0), "positive definite"); y1 = s1 \ x; norm(y1 - y0)
ans = 0

D.

```

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