Combining Explicit and Recursive Blocking for Solving Triangular Sylvester-Type Matrix Equations on Distributed Memory Platforms [chapter]

Robert Granat, Isak Jonsson, Bo Kågström
2004 Lecture Notes in Computer Science  
Parallel ScaLAPACK-style hybrid algorithms for solving the triangular continuous-time Sylvester (SYCT) equation AX − XB = C using recursive blocked node solvers from the novel high-performance library RECSY are presented. We compare our new hybrid algorithms with parallel implementations based on the SYCT solver DTRSYL from LAPACK. Experiments show that the RECSY solvers can significantly improve on the serial as well as on the parallel performance if the problem data is partitioned and
more » ... ted in an appropriate way. Examples include cutting down the execution time by 47% and 34% when solving large-scale problems using two different communication schemes in the parallel algorithm and distributing the matrices with blocking factors four times larger than normally. The recursive blocking is automatic for solving subsystems of the global explicit blocked algorithm on the nodes.
doi:10.1007/978-3-540-27866-5_97 fatcat:qnqd4po3dfd2rgglxd6hmimgum