ON HYPERBOLIC TRIANGULARIZATION - STABILITY AND PIVOTING

Authors
STEWART M STEWART GW
Citation
M. Stewart et Gw. Stewart, ON HYPERBOLIC TRIANGULARIZATION - STABILITY AND PIVOTING, SIAM journal on matrix analysis and applications, 19(4), 1998, pp. 847-860
Citations number
18
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on matrix analysis and applications → ACNP
ISSN journal
08954798
Volume
19
Issue
4
Year of publication
1998
Pages
847 - 860
Database
ISI
SICI code
0895-4798(1998)19:4<847:OHT-SA>2.0.ZU;2-X
Abstract
This paper treats the problem of triangularizing a matrix by hyperboli c Householder transformations. The stability of this method, which fin ds 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 ind ividual transformations are relationally stable. The analysis also sho ws that pivoting is required for the entire triangularization algorith m to be stable.