Parallel Algorithms for the Block Hessenberg Form and Applications

Abstract

In this paper we analyse the parallelisation of a stable algorithm for computing the controllable or observable part of a dynamic linear system. Our parallel algorithm is based on a numerically stable method that transforms the matrices of the system to block Hessenberg (or staircase) form. This algorithm requires one-sided orthogonal transformations and usual data layouts as 1-D and 2-D block column/row wrap are appropriate. The experimental results of the basic computational kernels on multicomputers show the degree of parallelism of this approach.