Randomized algorithms for total least squares problems

Xie, Peng; Xiang, Hua; Wei, Yimin

doi:10.1002/nla.2219

Cited by 32 publications

(25 citation statements)

References 58 publications

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“…Many important questions remain to be answered. Research on the interactions and combinations of SR with other techniques such as floating-point arithmetic [46], [47], randomized detection algorithms [31], [48], success probability analysis [49], [50], and numerous other topics is now being pursued.…”

Section: Discussionmentioning

confidence: 99%

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

Lyu¹,

Wen²,

Weng³

et al. 2020

IEEE Trans. Signal Process.

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Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for largescale problems, this paper investigates a new framework called sequential reduction (SR), which aims to reduce the lengths of all basis vectors. The performance upper bounds of the strongest reduction in SR are given when the lattice dimension is no larger than 4. The proposed new framework enables the implementation of a hash-based low-complexity lattice reduction algorithm, which becomes especially tempting when applied to large-scale MIMO detection. Simulation results show that, compared to other reduction algorithms, the hash-based SR algorithm exhibits the lowest complexity while maintaining comparable error performance.

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Section: Discussionmentioning

confidence: 99%

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

Lyu¹,

Wen²,

Weng³

et al. 2020

IEEE Trans. Signal Process.

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“…Thus, practical algorithms for approximating the condition numbers are worth studying. We propose statistical algorithms by taking advantage of the superiority of the small‐sample statistical condition estimation (SCE) techniques; see the details in other works …”

Section: Condition Numbers Of the Mtls Problemmentioning

confidence: 99%

“…We propose statistical algorithms by taking advantage of the superiority of the small-sample statistical condition estimation (SCE) techniques; see the details in other works. 19,[23][24][25] Perturbation analysis is an important research area in numerical analysis. Given a problem, the condition number measures the worst-case sensitivity of its solution to small perturbations in the input data.…”

Section: Theorem 3 Let H(a B) Be Defined As In Lemma 1 and Assume Tmentioning

confidence: 99%

Perturbation analysis for mixed least squares–total least squares problems

Zheng

Yang

2019

Numerical Linear Algebra App

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Summary In many linear parameter estimation problems, one can use the mixed least squares–total least squares (MTLS) approach to solve them. This paper is devoted to the perturbation analysis of the MTLS problem. Firstly, we present the normwise, mixed, and componentwise condition numbers of the MTLS problem, and find that the normwise, mixed, and componentwise condition numbers of the TLS problem and the LS problem are unified in the ones of the MTLS problem. In the analysis of the first‐order perturbation, we first provide an upper bound based on the normwise condition number. In order to overcome the problems encountered in calculating the normwise condition number, we give an upper bound for computing more effectively for the MTLS problem. As two estimation techniques for solving the linear parameter estimation problems, interesting connections between their solutions, their residuals for the MTLS problem, and the LS problem are compared. Finally, some numerical experiments are performed to illustrate our results.

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“…Jia and Yang improve our bounds of the approximation accuracy for severely, moderately and mildly ill-posed problems; see [23]. Randomized algorithms are also used for the generalized Hermitian eigenvalue problems by Saibaba et al [34] and for the TLS problem by Xie et al [45].…”

Section: Introductionmentioning

confidence: 99%

Randomized core reduction for discrete ill-posed problem

Zhang

Wei

2020

Journal of Computational and Applied Mathematics

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In this paper, we apply randomized algorithms to approximate the total least squares (TLS) solution of the problem Ax ≈ b in the large-scale discrete ill-posed problems. A regularization technique, based on the multiplicative randomization and the subspace iteration, is proposed to obtain the approximate core problem. In the error analysis, we provide upper bounds for the errors of the solution and the residual of the randomized core reduction.Illustrative numerical examples and comparisons are presented.

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Randomized algorithms for total least squares problems

Cited by 32 publications

References 58 publications

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

On Low-Complexity Lattice Reduction Algorithms for Large-Scale MIMO Detection: The Blessing of Sequential Reduction

Perturbation analysis for mixed least squares–total least squares problems

Randomized core reduction for discrete ill-posed problem

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