ANU Computer Science Technical Reports
Douglas R. Sweet and Richard P. Brent.
Error analysis of a partial pivoting method for structured
Shorter version to appear in Advanced Signal Processing Algorithms,
Proc. SPIE 40th Annual Meeting, San Diego, July 1995. (rpb157tr).
[POSTSCRIPT (144492 bytes)]
Abstract: (abridged) Many matrices that arise
in the solution of signal processing problems have a special
displacement structure. For example, adaptive filtering and
direction-of-arrival estimation yield matrices of Toeplitz type. A recent
method of Gohberg, Kailath and Olshevsky (GKO) allows fast Gaussian
elimination with partial pivoting for such structured matrices. We perform a
rounding error analysis on the Cauchy and Toeplitz variants of this method.
It is shown that the error growth can be much larger than that encountered
with normal Gaussian elimination with partial pivoting. A modification of the
algorithm to perform a type of row-column pivoting is proposed.
Technical Reports <Technical.Reports@cs.anu.edu.au>
Last modified: Tue May 13 14:55:38 EST 1997