Date: Wednesday November 9th 2022

Time: 11:00am to noon

Speaker: Lionel Eyraud-Dubois

Affiliation: Univ. Bordeaux, CNRS, Bordeaux INP, Inria, LaBRI, UMR

Title: Symmetric allocation schemes for distributed Cholesky factorization
Mode: Hybrid. Speaker will be in-person. Attendance can be in-person or remote.

Remote Attendance: contact mathstats-staff@ucdenver.edu for Zoom information

In-person Attendance: Student Commons Building, room 4113

Abstract: We consider the Cholesky factorization on a parallel distributed architecture. We present several results on the effect of allocation schemes on the volume of communication, showing how to take advantage of the symmetry of the access pattern. We show that the standard 2D block-cyclic allocation is not adapted to this symmetric operation, and propose a Symmetric Block Cyclic allocation scheme which significantly improves both communication volume and performance. We dive deeper into this question with a more theoretical approach, and obtain an improved sequential out-of-core lower bound on the communication volume. We also design a matching Triangular Block algorithm, which shows that the lower bound is optimal. Finally, we propose an adaptation of this algorithm to the parallel distributed setting, and we obtain further improvement both on communication volume and on performance.