Performance modeling of dense Cholesky factorization on the MasPar MP-2

In this paper we study various implementations of Cholesky factorization on SIMD architectures. A submatrix algorithm is implemented on the MasPar MP-2 using both block and torus-wrap data mappings. Both LL^T and LDL^T (square root free) implementations of the algorithm are investigated. The execution times and performance results for the MP-2 are presented. The performance of these algorithms is characterized in terms of the problem size, machine size and other machine dependent communication and computation parameters. Analysis for the communication and computation complexities for these algorithms is also presented, and models to predict the performance are derived. The torus-wrap mapped implementations outperformed the block approach for all problem sizes. The LDL^T implementation outperformed LL^T for small to medium problem sizes. © 1997 John Wiley & Sons, Ltd.