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 factorization routines—LU, QR, and Cholesky—included in the out-of-core extension of ScaLAPACK. These routines allow the factorization and solution of a dense system that is too large to fit entirely in physical memory. The full matrix is stored on disk and the factorization routines transfer sub-matrice panels into memory. The ‘left-looking’ columnoriented variant of the factorization algorithm is implemented to reduce the disk I/O traffic. The routines are implemented using a portable I/O interface and utilize high-performance ScaLAPACK factorization routines as in-core computational kernels. We present the details of the implementation for the out-of-core ScaLAPACK factorization routines, as well as performance and scalability results on a Beowulf Linux cluster. Copyright  2000 John Wiley & Sons, Ltd.