A Parallel Algorithm for Calculation of Large Determinants with High Accuracy for GPUs and MPI clusters

摘要

We present a parallel algorithm for calculating very large determinants witharbitrary precision on computer clusters. This algorithm minimises datamovements between the nodes and computes not only the determinant but also allminors corresponding to a particular row or column at a little extra cost, andalso the determinants and minors of all submatrices in the top left corner atno extra cost. We implemented the algorithm in arbitrary precision arithmetic,suitable for very ill conditioned matrices, and empirically estimated the lossof precision. The algorithm was applied to studies of Riemann's zeta function.