Old And New Algorithms For Toeplitz Systems

Richard P. Brent

doi:10.1117/12.948485

23 February 1988 Old And New Algorithms For Toeplitz Systems

Richard P. Brent

Proceedings Volume 0975, Advanced Algorithms and Architectures for Signal Processing III; (1988) https://doi.org/10.1117/12.948485
Event: 32nd Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1988, San Diego, CA, United States

Abstract

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" 0(n(log n)2) algorithms and compare them with 0(n2) algorithms.

Citation Download Citation

Richard P. Brent "Old And New Algorithms For Toeplitz Systems", Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); https://doi.org/10.1117/12.948485

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