Towards an Efficient Tile Matrix Inversion of Symmetric Positive Definite Matrices on Multicore Architectures

Details Towards an Efficient Tile Matrix Inversion of Symmetric Positive Definite Matrices on Multicore Architectures Towards an Efficient Tile Matrix Inversion of Symmetric Positive Definite Matrices on Multicore Architectures

2010-02-22

arxiv.org/abs/1002.4057v1

Computer Science

Mathematical Software

8 pages, extended abstract submitted to VecPar10 on 12/11/09, notification of acceptance received on 02/05/10. See: http://v

Scientific paper

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.

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