A weakly stable algorithm for general Toeplitz systems

Details A weakly stable algorithm for general Toeplitz systems A weakly stable algorithm for general Toeplitz systems

2010-05-04

arxiv.org/abs/1005.0503v1

Stability analysis of a general Toeplitz system solver, Numerical Algorithms 10 (1995), 225-244.

Mathematics

Numerical Analysis

17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143

Scientific paper

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.

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