Re: Socis 16 - Problem with pcg

[c.]

Dear Cris,

I don't know whether the info below is of any practical help
for your fixes to PCG but ...

On 3 Jul 2016, at 17:08, Cris <address@hidden> wrote:

> But it is not simple to determine if a general matrix A is positive definite. 
> A way to determine it is to compute the eigenvalues of A (indeed an 
> equivalent condition is to have all the eigenvalues real and positive), but 
> it is not practicable if the matrix is very big.

I think the most efficient way to check whether a matrix is SPD is to attempt a 
Cholesky decomposition.
If the decomposition completes successfully the matrix is SPD, otherwise it is 
not.

Of course this is of no help in implementing PCG because if you can decompose 
the matrix you 
can solve the ystem by a direct method, no need to do PCG iteration...

>  Also in the Octave/Matlab pcg code, A can be passed as a function handle and 
> we can not compute the eigenvalues of a function handle.

Actually 'eigs' can compute the eigenvalues of a matrix passed as a function 
handle.

c.