Remarks on a displacement-rank inversion method for Toeplitz systems

Sexton, H.; Shensa, M.; Speiser, Jeffrey M.

doi:10.1016/0024-3795(82)90215-4

Cited by 12 publications

(8 citation statements)

References 4 publications

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“…5 Fast algorithms with complexity O(L(logL) ) have been developed to solve a Toeplitz linear equation [37]- [39]. However, it has been shown that the constant hidden in the "O" notation for such algorithms is so large that they are actually faster than the O(L ) algorithms only when L is very large [38], [39]. For this reason, they are also called "asymptotically fast" algorithms [39].…”

Section: Least Squares Estimationmentioning

confidence: 99%

A Frequency Domain State-Space Approach to LS Estimation and Its Application in Turbo Equalization

Guo

Huang

2011

IEEE Trans. Signal Process.

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A frequency domain state-space approach to the least squares (LS) estimation for finite impulse response (FIR) system identification is proposed by exploiting the Toeplitz structure of the data matrix, leading to two low-complexity FFT (fast Fourier transform)-based unbiased recursive estimators. The proposed recursive estimators are applied to the smoothing estimation of timevarying frequency selective channels in turbo equalization systems, and channel estimation approaches with complexity (log ) per symbol are developed, where is the number of channel taps.

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Section: Least Squares Estimationmentioning

confidence: 99%

A Frequency Domain State-Space Approach to LS Estimation and Its Application in Turbo Equalization

Guo

Huang

2011

IEEE Trans. Signal Process.

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“…Sexton et al 49 evaluated the constant hidden in the "O" notation for an asymptotically fast algorithm based on the concept of displacement rank, 5 and found that the constant was so large that the algorithm was impractical. More recent asymptotically fast algorithms, such as that of de Hoog, 29 appear to have a smaller constant.…”

Section: 103235mentioning

confidence: 99%

Old And New Algorithms For Toeplitz Systems

Brent

1988

SPIE Proceedings

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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(n 2 ) algorithms.

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“…Sometimes these algorithms are called superfast [1]. We avoid this terminology because, even though the algorithms require only O(n(log n) 2 ) arithmetic operations, they may be slower than O(n 2 ) algorithms for n < 256 (see [1,20,68]). We prefer the term asymptotically fast.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a general toeplitz systems solver

1995

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We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R T R is close to A T A. Thus, when the algorithm is used to solve the semi-normal equations R T Rx = A T b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min Ax − b 2 .

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Remarks on a displacement-rank inversion method for Toeplitz systems

Cited by 12 publications

References 4 publications

A Frequency Domain State-Space Approach to LS Estimation and Its Application in Turbo Equalization

A Frequency Domain State-Space Approach to LS Estimation and Its Application in Turbo Equalization

Old And New Algorithms For Toeplitz Systems

Stability analysis of a general toeplitz systems solver

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