On hyperbolic triangularization: Stability and pivoting

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.