A Scalable Parallel Block Algorithm for Band Cholesky Factorization.
R. C. Agarwal, Fred G. Gustavson, Mahesh V. Joshi, Mohammad Zubair · 1995
In this paper, we present an algorithm for computing the Cholesky factorization of large banded matrices on the IBM distributed memory parallel machines. The algorithm aims at optimizing the single node performance and minimizing the communication overheads. An important result of our paper is that the proposed algorithm is strongly scalable. As the bandwidth of the matrix increases, the number of processors that can be efficiently utilized has a quadratic relationship. 1 Introduction Many of the matrices arising from large scientific applications have a banded structure. Banded solvers, as opposed to dense solvers, are difficult to parallelize because of their lower computation to communication ratios. Therefore, algorithms for such problems need to employ special techniques to reduce communication overheads. Several researchers have investigated parallel algorithms for solving band systems [2, 3, 4, 5, 6, 7, 8]. Most of these algorithms are either developed for special purpose arch...