I have a big linear system of ~ $5000$ unknowns.
It is a symbolic problem in the sense that I need to find exact solutions, but I don't have variables, everything is a number (If I represent the matrix of the system it is a matrix full of symbolic numbers, not variables).
(By the way if there is a name for "symbolic but numbers", I would appreciate to know it).
It seems to be too long for my computer, so I am asking :
- Do you think such a problem is feasible on a standard computer ?
- What are the techniques I could use to increase the speed of computation at the maximum (can I parallelize, can I do other things that I don't know to increase at the maximum the speed ?)
Note : The matrix of the problem is dense.