On 04/04/2017 19:05, Dima Pasechnik wrote:
On Tuesday, April 4, 2017 at 3:02:46 PM UTC+1, vdelecroix wrote:
Dear all,
I am currently solving huge sparse linear systems over rationals (up to
millions of equations and variables). The equation are actually
integral, but the solutions are rationals.
Sage is doing pretty good up to dimension 1000 with the generic
solve_right method. Where should I look for libraries implementing
somethig less naive?
I would look at linear programming solvers.
How big are your integer coefficients?
Very small (<~ 10). And the matrix is very sparse: n log(n) terms for
size n x n (though my matrices are not square).
As well, typically large systems are solved by iterative methods, the
problem
is that it's usually floating point implementations.
One important point: I know by construction that the solution is unique!
Rational reconstruction still applies for floating point and it is easy
to check that the reconstruction is actually correct. Might be
reasonable to first try with floating point.
Vincent
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