QR factorization of Toeplitz matrices
92. A. W. Bojanczyk, R. P. Brent and F. R. de Hoog,
QR factorization of Toeplitz matrices,
Numerische Mathematik 49 (1986), 81-94.
Also appeared as
Report CMA-R07-85, Centre for Mathematical Analysis, ANU, May 1985.
This paper presents a new algorithm for computing the QR factorization
of an m x n Toeplitz matrix in
The algorithm exploits procedures for the rank-1 modification
of a Cholesky factorisation 
and the fact that both principal
(m-1) x (n-1)
submatrices of the Toeplitz matrix are identical.
An efficient parallel implementation of the algorithm is possible.
The algorithm described here is more stable
numerically than that of
Sweet [Numerische Mathematik 43 (1984), 1-21].
As noted in ,
the factor R in the orthogonal
factorization T = QR
is computed about as well as would be
expected from a Cholesky factorization of TTT.
However, the computed Q is not necessarily close to orthogonal.
For related work, see
Go to next publication
Return to Richard Brent's index page