VSPAERO has multiple convergence loops.
In a normal solve, there are two main loops. There is a nonlinear convergence loop that iterates over the wake position and the stall factor. Inside of that loop, there is an iterative matrix solution.
The Non-linear factor is a scale factor applied to the default tolerance for the nonlinear convergence loop. Set it to .01 to converge two orders tighter than the default tolerance. Making this smaller will increase the number of wake iterations (for example).
The Forward MAT factor is a scale factor applied to the default tolerance for the inner matrix solution.
Similarly, there is an iterative matrix solution loop that applies to solving the adjoint equations when that is needed. The Adjoint MAT factor adjusts that tolerance.
The core size is not presently used, it does nothing right now.
Rob