On the solution of block Hessenberg systems

TitleOn the solution of block Hessenberg systems
Publication TypeJournal Articles
Year of Publication1995
AuthorsStewart G.W
JournalNumerical Linear Algebra with Applications
Pagination287 - 296
Date Published1995/05/01/
ISBN Number1099-1506
Keywordsblock Hessenberg matrix, Block Toeplitz matrix, linear system, queue

This paper describes a divide-and-conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.