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I am dealing with a large sparse integer matrix that I need to find the nullspace of. I've seen Markowitz Pivoting come up in several places discussing similar problems such as here:

http://www.mapleprimes.com/posts/41191-Solving-Sparse-Linear-Systems-In-Maple

And in the MAGMA documentation under the sparse null space algorithm. How can one use this technique (or similarly perhaps, the Structured Gaussian Elimination mentioned above it) to reduce a sparse matrix to a dense, small matrix? I understand that you can eliminate variables with regular Gaussian Elimination, but how does one retrieve those after solving the new system?

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  • $\begingroup$ How large is this matrix? A sparse QR or sparse SVD algorithm will be more numerically stable than sparse LU. If your matrix is very large, iterative procedures also exist. $\endgroup$ – Geoff Oxberry Feb 19 '14 at 19:46
  • $\begingroup$ Sorry, the system is integer, so the algorithm should be exact. I edited it into the question. $\endgroup$ – RobVerheyen Feb 19 '14 at 19:59
  • $\begingroup$ I am currently working on a matrix with size 12000, but I'd like to be able to go bigger later. $\endgroup$ – RobVerheyen Feb 19 '14 at 20:10

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