The design and implementation of the parallel out-of-core ScaLAPACK LU, QR, and Cholesky factorization routines

This paper describes the design and implementation of three core LU, QR and Cholesky factorization routines included in the out-of-core extension of ScaLAPACK. These routines allow the factorization and solution of a very large dense system that is too large to t entirely in physical memory. An image of the full matrix is maintained on disk and the factorization routines transfer sub-matrices to be operated in memory. A `left-looking' column-oriented variant of the factorization algorithm is implemented to reduce the disk I/O tra c. The routines are implemented using a portable I/O interface and uses high performance ScaLAPACK factorization routines as in-core computational kernels. We present the details of the implementation of the out-of-core ScaLAPACK factorization routines as well as performance and scalability results on the Intel Paragon.

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