A weakly stable algorithm for general Toeplitz systems
A weakly stable algorithm for general Toeplitz systems
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.
17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.html
65F05 (Primary) 15B05, 65G50 (Secondary), FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), F.2.1
65F05 (Primary) 15B05, 65G50 (Secondary), FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), F.2.1
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