I have a linear system that I want to solve with Matlab using linsolve. My problem is that the coefficients' range of the system is huge. The minimum coefficient start at e-20 while the max reach 10e25. When I use linsolve, I get a warning telling me "Warning: Rank deficient, rank = 15, tol = 5.2711e+005.". When I use rank on my system, I effectively observe that my system is not full rank. But when I use rank(sys, tol) with a small tol value (~e-15), I obtain a full rank system.
So I suppose that linsolve choose a tolerance that is to high for my system and my question is if there exists a way to specify a tolerance value to linsolve in ordre to solve system with a high range of coefficients.