Symbolic inverse of large matrices

I have a system of differential equations in mass matrix form: M*x_dot = F and I want to find out the solution. In my case M and F are nonlinear and contain symbolic variables. Using M\F or inv(M)*F takes too long to compute. Is there a faster way to solve this problem?

Answer 1

[Walter Roberson]

No, symbolic computation like that often takes a long long time; it becomes completely impractical with even fairly moderately sized matrixes (e.g, 35 x 35 is much too much.)

You can really only make improvements in the computation if M is (truly) sparse, or if M has special properties such as being tri-diagonal. The inverse of a sparse symbolic matrix is generally dense, but the length of the expressions get cut way way down if there are a lot of 0s.