Comparison theorems of preconditioned Gauss–Seidel methods for M-matrices

Yuan, Jinying; Zontini, Diego Dutra

doi:10.1016/j.amc.2012.08.037

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…Next we show that the proposed detector with the proposed preconditioner converges faster than the conventional GS and preconditioned GS detectors. The following theorem [38] should be introduced before the mathematical derivations.…”

Section: Convergence Comparisonmentioning

confidence: 99%

\mathbf {A}\ge 0

be a square matrix. Then, (i) It has a positive real eigenvalue equal to its spectral radius.…”

Section: Proposed Detector For Ls‐mimo Systemsmentioning

confidence: 99%

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Improved Gauss–Seidel detector for large‐scale MIMO systems

et al. 2022

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Large-scale multiple-input multiple-output (LS-MIMO) is one of the promising technologies beyond the 5G cellular system in which large antenna arrays at the base station (BS) improve the system capacity and energy-efficiency. However, the large number of antennas at the BS makes it challenging to design low-complexity high-performance data detectors. Thus, a number of iterative detection methods, such as Gauss-Seidel and conjugate gradient, are introduced to achieve complexity-performance tradeoff. However, their performance deteriorates for the systems with small BS-to-user antenna ratio or for the channels that exhibit correlation. This paper proposes a new efficient iterative detection algorithm based on the improved Gauss-Seidel iteration to address this problem. The proposed method performs one conjugate gradient iteration that enables better performance with less number of iterations. A new hybrid iteration is introduced and a low-complexity initial estimation is utilised to enhance detection accuracy while reducing the complexity further. In addition, a novel preconditioning technique is proposed to maintain the benefits of the proposed detector in correlated MIMO channels. It is mathematically demonstrate that the proposed detector achieves low approximated error. Theoretical analysis and numerical results show that the proposed algorithm provides a faster convergence rate compared to conventional methods.

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Section: Convergence Comparisonmentioning

confidence: 99%

\mathbf {A}\ge 0

be a square matrix. Then, (i) It has a positive real eigenvalue equal to its spectral radius.…”

Section: Proposed Detector For Ls‐mimo Systemsmentioning

confidence: 99%

Improved Gauss–Seidel detector for large‐scale MIMO systems

et al. 2022

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show abstract

“…The comparisons between either different preconditioners or different parameters of a same type preconditioner have investigated by many authors in [1,2,14,15,18,19,29,26,27,33,36,38,41,42,44,53,56,59,60,62,63,64,65,66,68,72,80,81,82,83,85,89,90,91,94,97]. This is an important and interesting research subject.…”

Section: 43)mentioning

confidence: 99%

“…It is continued to study in [22]. It is proposed in [89,94] for the preconditioned Gauss-Seidel method, where…”

Section: Another Combination Is Given Asmentioning

confidence: 99%

On preconditioned AOR method for solving linear systems

Song¹

2020

Preprint

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In this paper, we investigate the preconditioned AOR method for solving linear systems. We study two general preconditioners and propose some lower triangular, upper triangular and combination preconditioners. For A being an L-matrix, a nonsingular M-matrix, an irreducible L-matrix and an irreducible nonsingular M-matrix, four types of comparison theorems are presented, respectively. They contain a general comparison result, a strict comparison result and two Stein-Rosenberg type comparison results. Our theorems include and are better than almost all known corresponding results.

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A new family of (I+S)-type preconditioner with some applications

Najafi

Edalatpanah

2014

Comp. Appl. Math.

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Comparison theorems of preconditioned Gauss–Seidel methods for M-matrices

Cited by 7 publications

References 11 publications

Improved Gauss–Seidel detector for large‐scale MIMO systems

Improved Gauss–Seidel detector for large‐scale MIMO systems

On preconditioned AOR method for solving linear systems

A new family of (I+S)-type preconditioner with some applications

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