Hi.

One of my students is solving some large sparse systems (more than 20K 
equations). The coeficient matrix 
is symmetric and positive definite, with large sparsivity (1% of non zero 
elements in some cases).

After playing around a little bit with cholfact we decided to compare the 
time with a very simple implementation
of the conjugate gradient method with diagonal scaling. 

The code is in

https://gist.github.com/CodeLenz/92086ba37035fe8d9ed8#file-gistfile1-txt

And, as for example, the solution of Ax=b for 

julia> A = sprand(10000,10000,0.01); A = A'+A; 
A=A+100*rand()*speye(10000,10000)

takes 16 seconds with cholfact(A) and 600 milliseconds !!! with DCGC 
(tol=1E-10)

Also, as expected, the memory consumption with CG is very low, allowing the 
solution 
of very large systems. 

The same pattern is observed for different leves of sparsivity and for 
different random matrices.

I would like to thank the Julia developers for such amazing tool !



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