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.
© (1988) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Richard P. Brent, Richard P. Brent, "Old And New Algorithms For Toeplitz Systems", Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); doi: 10.1117/12.948485; https://doi.org/10.1117/12.948485

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