## How can I create sparse symmetric positive definite linear system?

### D (view profile)

on 6 Aug 2013
Latest activity Commented on by sai chand

on 17 Jul 2019

### Richard Brown (view profile)

Dear All :) I'm looking for sparse symmetric positive definite linear system Ax=b. Is it possible to generate it in Matlab? I need matrix A about 50x50 (maximum 100x100 - minimum 20x20) and vector b. It might be floating point numbers... I prefer not compressed format ;)
D.

### Richard Brown (view profile)

on 6 Aug 2013
Edited by Richard Brown

### Richard Brown (view profile)

on 6 Aug 2013

sprandsym is what you want.
m = 50;
density = 2/m; % for example
rc = 0.1; % Reciprocal condition number
A = sprandsym(m, density, rc, 1);
If you don't want it in compressed column format
A = full(A);
Verify positive definiteness
chol(A);

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Richard Brown

### Richard Brown (view profile)

on 7 Aug 2013
Not directly, but you might try scaling and rounding results from sprandsym, or something like that
sai chand

### sai chand (view profile)

on 17 Jul 2019
How to generate the matrix b.
Can it be a random one independent of the way A is generated?
sai chand

### sai chand (view profile)

on 17 Jul 2019
I needed to generate a symmetric sparse positive definite matrix. can you help me in that?