Has anyone used a non-FORTRAN, non-commercial (including MATLAB) general sparse matrix subroutine library that they would recommend?

For special cases, one can surely think of a series of transformations to change the column ordering individually. But such transformations would not be orthogonal and full rank. The advantage of a permutation matrix is that it is trivially full rank (its columns are basis vectors) and orthogonal. Thus, we only consider entire column and row orderings, not for individual elements.

Edited by author 11-30-2004 11:50 AM
Rasit,
re - change column ordering of rows individually -
I don't think you could do that without changing the matrix.

Would a low bandwidth be more adventageous at all times?

Would it be possible to change column ordering of rows individually to put a matrix into a band structure?

Edited by author 11-29-2004 09:57 PM
Stephen, the parts I will cover will mostly deal with graph theoretic approaches to dealing with sparsity. The relevant parts from the text would be Section 6.4 onwards, but some earlier results will be needed. Since it is a short presentation, I don't think I will be able to cover banded sparse systems. So the talk should be limited to general sparse systems.

The text uses results from graph theory, the proofs can be found in papers by R.E.Tarjan, such as "Graph Theory and Gaussian Elimination" and "Algorithmic Aspects of Vertex Elimination on Directed Graphs" by D.J.Rose and R.E. Tarjan.

Edited by author 11-29-2004 09:46 PM
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This is quite dense. If you had a specific sparse matrix type, it would be useful to apply the appropriate method. Is there a specific method that you're interested in for your work, or is you interest more general?