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\title{Numerical Stability of Some Fast Algorithms for Structured Matrices}
\author{Richard Brent \\
Computer Sciences Laboratory\\ Research School of Information 
Sciences and Engineering \\ Australian National University \\
Canberra, ACT 0200, Australia }
\date{}
\maketitle
We consider the numerical stability/instability of fast algorithms for solving
systems of linear equations or linear least squares problems with a low
displacement-rank structure. For example, the matrices involved may be
Toeplitz or Hankel.  In particular, we consider algorithms which incorporate
pivoting without destroying the structure, such as the GKO algorithm, and
describe some recent results by Brent and Sweet, Ming Gu, Michael Stewart
and others on the stability of these algorithms.  It is interesting to compare
these results with the corresponding stability results for algorithms based on
the seminormal equations and for the well known algorithms of Levinson
type and Bareiss/Schur type. 
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