A weakly stable algorithm for general Toeplitz systems
Numerical Analysis
2015-05-18 v1 Numerical Analysis
Abstract
We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.
Cite
@article{arxiv.1005.0503,
title = {A weakly stable algorithm for general Toeplitz systems},
author = {Adam W. Bojanczyk and Richard P. Brent and Frank R. de Hoog},
journal= {arXiv preprint arXiv:1005.0503},
year = {2015}
}
Comments
17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.html