I believe Spars mean sparse matrix and not an equation solver.
A sparse matrix occurs if one names the nodes without the due consideration to minimise the storage. Modern software would re-name the nodes interanlly to make the system more compact to reduce storage as well as cut down computation time. When the solution is done the information is converted back to user's convention without him knowing what has happened in between.
Couldn't tell what is inside Nastran. I believe for huge out-of-core equation solvers there are exact method like Guassian elimination. For semi-iterative there is Guassian-Seidel method. Never tried the iterative scheme myself but I suppose it could be the iterative schemes for the matrix inversion.