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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: 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


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