Old and new algorithms for Toeplitz systems

108. R. P. Brent, Old and new algorithms for Toeplitz systems, Proceedings SPIE, Volume 975, Advanced Algorithms and Architectures for Signal Processing III (edited by Franklin T. Luk), SPIE, Bellingham, Washington, 1989, 2-9.

Abstract: dvi (3K), pdf (67K), ps (27K).

Paper: dvi (22K), pdf (114K), ps (59K).


Toeplitz linear systems and Toeplitz least squares problems commonly arise in digital signal processing. In this paper we survey some old, "well known" algorithms, and some recent algorithms, for solving these problems. We concentrate our attention on algorithms which can be implemented efficiently on a variety of parallel machines (including pipelined vector processors and systolic arrays). We distinguish between algorithms which require inner products, and algorithms which avoid inner products, and thus are better suited to parallel implementation on some parallel architectures. Finally, we mention some "asymptotically fast" O(n(log n)2) algorithms and compare them with O(n2) algorithms.


A revision appeared as [111]. For more recent results, see Brent et al [ 143, 144, 177].

Go to next publication

Return to Richard Brent's index page