Longer version: Error analysis of a partial pivoting method for structured matrices, Technical Report TR-CS-95-03, Computer Sciences Laboratory, ANU, June 1995, 20 pp. arXiv:1005.0667v1
Related talk presented at a Workshop on Numerical Methods for Structured Matrices in Filtering and Control, Santa Barbara, August 1996.
Conference Paper: dvi (33K), pdf (230K), ps (97K).
Technical Report: dvi (38K), pdf (242K), ps (143K).
Transparencies (Santa Barbara, August 1996): dvi (21K), pdf (235K), ps (152K).
In this paper, a rounding error analysis is performed on the Cauchy and Toeplitz variants of the GKO method. It is shown the error growth depends on the growth in certain auxiliary vectors, the generators, which are computed by the GKO algorithms. It is also shown that in certain circumstances, the growth in the generators can be large, and so the error growth is much larger than would be encountered with normal Gaussian elimination with partial pivoting. A modification of the algorithm to perform a type of row-column pivoting is proposed; it may ameliorate this problem.
For subsequent attempts by Ming Gu and Michael Stewart to improve the stability of the GKO algorithm, and results on the stability of the generalised Schur algorithm, see  and the references given there.
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