Solving large linear systems

2011 6 9
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Hello,
I want to solve a large system Ax=b, the size of A is 300,000, the matrix is sparse and diagonal dominant.
Backslash is not more viable, so I'm trying to use "ilu" and "luinc" as a preconditioner within an iterative solver (bicg, gmres, pcg) but I get "out of memory" in the ilu/luinc computation.
Is there any suggestion you could give me? Is there any other function?
Thank you!

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What makes you think that backslash is not viable?
Hugo
Hugo 2011-6-9
Because I got "out of memory" and the error seemed to be in: "mldivide"
Andrew Newell
Andrew Newell 2011-6-10
By "size", do you mean each dimension?

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Andrew Newell
Andrew Newell 2011-6-10

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With the information you have provided, it is difficult to diagnose your problem. Do you get an "out of memory" error if you run the following commands?
n = 300000;
e = rand(n,1);
A = spdiags([e -2*e e], -1:1, n, n);
b = rand(n,1);
y = A\b;
EDIT: Here is code based on the new details you have provided:
N = 700;
B = 1e6*ones(N*N,3);
d = [-N 0 N]; % This might be [-N-1 0 N+1], depending on what "separate" means
Z = spdiags(B,d,N*N,N*N);
H = rand(N*N,1);
Y=Z\H;
This took my computer 2.3 seconds and I had no memory problems.

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Hugo
Hugo 2011-6-15
Thanks for your answer, I tried your example and I don't have any problem solving it, but I don't know why with my system I get "out of memory". Let me tell you what I have:
N = 700
Z = spalloc(N*N,N*N,nnz) % Z almost [500,000 x 500,000]
H = full vector [500,000 x 1]
for x = 1:N
for y = 1:N
Z = Computation of Z;
end
end
% The matrix Z is diagonal, symmetric, sparse,
% all of its values are "10e+6", its form is three diagonal lines in the diagonal, one in the right side and one in the left side, both last ones separate from the center diagonal 700 points (hope this is clear)
Y = Z\H : Out of memory
[L,U] = luinc(Z,1e-7); : Out of memory
[H,flag,relres,iter,resvec] = pcg(Z,H,1e-6,100,L,U);
Is there any other preconditioner I could use?
Thank you!!!
John D'Errico
John D'Errico 2011-6-15
By the way, if you are generating a tridiagonal banded matrix using a spalloc and a loop, then you need to learn how to use spdiags.
Hugo
Hugo 2011-6-17
Hi Andrew,
I tried your example and you're right, I had no problem at all, but I made a mistake and I forgot to say that my matrix is complex, so using your example I ran this one and I got "out of memory".
N = 700;
B = 1e6*ones(N*N,5) + 1i*1e6*ones(N*N,5);
d = [-N -1 0 1 N];
Z = spdiags(B,d,N*N,N*N);
figure(1), spy(Z)
H = 1e6*ones(N*N,1);
Y=Z\H;
The matrix is around 50MB. Do you have any other idea of what can I do? I would really appreciate it!! I tried iterative but building the preconditioner "luinc" gave me again "out of memory"
Thanks!!
Hugo
Hugo 2011-6-17
BTW, the matrix is tridiagonal with two band off-diagonals separate N (N=700)

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