Richard P. Brent
Published 2010-05-05Version 1
We survey the numerical stability of some fast algorithms for solving systems of linear equations and linear least squares problems with a low displacement-rank structure. For example, the matrices involved may be Toeplitz or Hankel. We consider algorithms which incorporate pivoting without destroying the structure, and describe some recent results on the stability of these algorithms. We also compare these results with the corresponding stability results for the well known algorithms of Schur/Bareiss and Levinson, and for algorithms based on the semi-normal equations.
Comments: 13 pages. An old Technical Report (CSL, ANU, September 1997, 13 pages), submitted for archival purposes. For further details see http://wwwmaths.anu.edu.au/~brent/pub/pub177.html
Journal: "Fast Reliable Algorithms for Matrices with Structure" (edited by Ali Sayed and Thomas Kailath), SIAM, Philadelphia, 1999, 103-116
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