On Hyperbolic Triangularization: Stability and Pivoting

Authors:
Michael Stewart;G. W. Stewart
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1998

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Abstract

This paper treats the problem of triangularizing a matrix by hyperbolic Householder transformations. 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 general 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.