Parallel algorithms and condition estimators for standard and generalized triangular sylvester-type matrix equations

Abstract

We discuss parallel algorithms for solving eight common standard and generalized triangular Sylvester-type matrix equation. Our parallel algorithms are based on explicit blocking, 2D block-cyclic data distribution of the matrices and wavefront-like traversal of the right hand side matrices while solving small-sized matrix equations at different nodes and updating the rest of the right hand side using level 3 operations. We apply the triangular solvers in condition estimation, developing parallel sep-1-estimators. Some experimental results are presented. © Springer-Verlag Berlin Heidelberg 2007.