I need to implement parallel dense matrix inversion for a language I am using that appears to not have an existing library for this (specifically IDL using IDL Bridge for message passing). I am familiar with parallel programming methods through experience using MPI in C++, though mainly for parallel FFT and N-body methods. I have little experience or knowledge of computational methods, serial or parallel, for linear algebra.
What I am looking for is a clear pseudo code description of a robust, stable parallel matrix inversion algorithm that is appropriate for a small number of cores as the machine that runs the (currently serial) IDL task has 8 cores. In practice I will probably use only 4 to keep cores free for other tasks.
I'd favour simplicity over bleeding edge performance if there are a range of well known algorithms for this task.