On hyperbolic triangularization: Stability and pivoting

TitleOn hyperbolic triangularization: Stability and pivoting
Publication TypeJournal Articles
Year of Publication1998
AuthorsStewart M, Stewart G.W
JournalSIAM journal on matrix analysis and applications
Pagination847 - 860
Date Published1998///

This paper treats the problem of triangularizing a matrix by hyperbolic Householdertransformations. The stability of this method, which finds application in block updating and fast
algorithms for Toeplitz-like matrices, has been analyzed only in special cases. Here we give a gen-
eral analysis which shows that two distinct implementations of the individual transformations are
relationally stable. The analysis also shows that pivoting is required for the entire triangularization
algorithm to be stable.