I have a general square dense matrix A (not symmetric) which is formed by A=P^{T}BP where B was in a compressed storage scheme and P is a rectangular matrix. The size of A ranges from 10x10 to 500x500, where B can be 150,000x150,000 and is sparse.

What would be the best way to solve for x given b (system of linear equations) that result from

Ax=b => x=A^{-1}b

Right now I am just using LAPACK DGESV that is linked to MKL (so assume I am using their solver). Is there any benifit to going to a interative solver or any recomendations as to how to best solve this system of equations as fast as possible.

Thanks for any comments