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Static storage of huge sparce matrices

From: Joza
Subject: Static storage of huge sparce matrices
Date: Fri, 2 Nov 2012 10:50:39 -0700 (PDT)

To implement a Successive Over Relaxation scheme to iteratively solve Ax = b,
I want to statically store the sparse square matrix A which has dimensions
1000 X 1000.

The diagonal element of A is 2, and the next higher and lower off-diagonals
are both -1. All other elements are zero. Of course, in the first row, there
is no next lower off-diagonal, and no next higher off-diagonal in the last

Obviously, there is no point storing all those zeros. I know that one can
use three arrays to start the elements. ARRAY_1 will store the non-zeros,
ARRAY_2 will store the columns to which the values in ARRAY_1 correspond,
and ARRAY_3 stores where each row begins in ARRAY_1. 

I have no idea how I go about implementing these three arrays. How can I
create them? I know Octave has some nice functions for dealing with sparse
matrices - are there functions that I can use for this purpose?

As always, thanks for all the help, you geniuses!! :

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