  The algorithms in the current sequential numerical linear algebra libraries
(e.g. LAPACK) do not parallelize well on multicore architectures. A new family
of algorithms, the tile algorithms, has recently been introduced. Previous
research has shown that it is possible to write efficient and scalable tile
algorithms for performing a Cholesky factorization, a (pseudo) LU
factorization, and a QR factorization. In this extended abstract, we attack the
problem of the computation of the inverse of a symmetric positive definite
matrix. We observe that, using a dynamic task scheduler, it is relatively
painless to translate existing LAPACK code to obtain a ready-to-be-executed
tile algorithm. However we demonstrate that non trivial compiler techniques
(array renaming, loop reversal and pipelining) need then to be applied to
further increase the parallelism of our application. We present preliminary
experimental results.
