STABILITY ANALYSIS OF FAST TOEPLITZ LINEAR SYSTEM SOLVERS

A. W. BOJANCZYK, R. P. BRENT, AND F. R. DE HOOG

Abstract

We present a numerical stability analysis of the Bareiss and Levinson algorithms for solving a symmetric positive definite Toeplitz system of linear equations.

Comments

Only the Abstract is given here. The full report appeared as [1]. For a revision, see [2].

References

1. A. W. Bojanczyk, R. P. Brent and F. R. de Hoog, Stability Analysis of Fast Toeplitz Linear System Solvers, Report CMA-MR17-91, Centre for Mathematical Analysis, ANU, August 1991, 23 pp. rpb126tr.

2. A. W. Bojanczyk, R. P. Brent, F. R. de Hoog, and D. R. Sweet, “On the stability of the Bareiss and related Toeplitz factorization algorithms”, SIAM J. Sci. Computing, to appear. rpb144.

(Bojanczyk) School of Electrical Engineering, Cornell University, Ithaca, NY 14853

(Brent) Computer Sciences Laboratory, Australian National University, Canberra

(de Hoog) CSIRO Division of Mathematics and Statistics, GPO Box 1965, Canberra, ACT 2601

1991 Mathematics Subject Classification. Primary 65F05; Secondary 47B35, 65F30, 65Y05, 65Y10. Key words and phrases. Toeplitz matrix, Bareiss algorithm, Levinson algorithm, positive-definite ma-

trix, symmetric matrix.

Copyright \begin{matrix}c \\ ◯ \end{matrix} 1991, the authors. Comments \begin{matrix}c \\ ◯ \end{matrix} 1993, R. P. Brent. rpb126a typeset using AMS-L^{A}TEX