High Accuracy Matrix Computations on Neural Engines: A Study of QR Factorization and its Applications

Zhang, Shaoshuai; Baharlouei, Elaheh; Wu, Panruo

doi:10.1145/3369583.3392685

Cited by 9 publications

(2 citation statements)

References 19 publications

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“…It would also be worth investigating the extension of this work to other matrix factorization algorithms, in particular QR factorization. Indeed, to our knowledge, existing mixed precision QR algorithms (Yang et al, 2021; Zhang et al, 2020) also assume the matrix to be stored in fp32 precision; the ideas proposed here could be extended so as to store them in fp16.…”

Section: Discussionmentioning

confidence: 99%

Mixed precision LU factorization on GPU tensor cores: reducing data movement and memory footprint

Lopez

Mary²

2023

The International Journal of High Performance Computing Applica

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Modern GPUs equipped with mixed precision tensor core units present great potential to accelerate dense linear algebra operations such as LU factorization. However, state-of-the-art mixed half/single precision LU factorization algorithms all require the matrix to be stored in single precision, leading to expensive data movement and storage costs. This is explained by the fact that simply switching the storage precision from single to half leads to significant loss of accuracy, forfeiting all accuracy benefits from using tensor core technology. In this article, we propose a new factorization algorithm that is able to store the matrix in half precision without incurring any significant loss of accuracy. Our approach is based on a left-looking scheme employing single precision buffers of controlled size and a mixed precision doubly partitioned algorithm exploiting tensor cores in the panel factorizations. Our numerical results show that compared with the state of the art, the proposed approach is of similar accuracy but with only half the data movement and memory footprint, and hence potentially much faster: it achieves up to 2× and 3.5× speedups on V100 and A100 GPUs, respectively.

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Section: Discussionmentioning

confidence: 99%

Mixed precision LU factorization on GPU tensor cores: reducing data movement and memory footprint

Lopez

Mary²

2023

The International Journal of High Performance Computing Applica

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“…The LR factorization can be utilized in parallel computation [5][6][7], applied in many engineering and technology needs like data movement analysis and circuit simulation [8][9][10]. Due to the special attributes of the orthogonal matrix after the QR factorization, the computation is more efficient and stable, often applied in least squares problems and optimization problems [11,12], in real life like the smart grid, pathological matrix problems, harmonic compensation of inductors and other aspects of important performance [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

AREND: A Faster and Robust Solution for Dynamic LR and QR Factorization

Zhuang,

He,

et al. 2024

Preprint

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Dynamic LR and QR factorization are fundamental problems that exist widely in the control field. However, the existing solutions under noises are lack of convergence speed and anti-interference ability. To this end, this paper incorporates the advantages of Dynamic-Coefficient Type (DCT) and Integration-Enhance Type (IET) Zeroing Neural Dynamic (ZND), and proposes an Adaptive and Robust-Enhanced Neural Dynamic (AREND). On this basis, a Strategy of Integration-Coupling (SIC) is proposed to address multiple error function problems, improving model stability and application scenarios. This strategy is experimentally proven to be effective and has potential expansion capability. After that, the convergence and robustness of our AREND is theoretically analyzed. Furthermore, the proposed AREND is verified by numerical experiments of low-to-high dimensional factorization in comparison with existing solutions. Finally, the real-time 3-D Angle of Arrival (AoA) localization in multiple high-noise conditions, is validated to the accuracy of the proposed model. Code is available at https://github.com/Alana2a3/AREND-Code-Implementation.

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Exact QR factorizations of rectangular matrices

Lourenco,

Moreno-Centeno

2024

Optim Lett

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High Accuracy Matrix Computations on Neural Engines: A Study of QR Factorization and its Applications

Cited by 9 publications

References 19 publications

Mixed precision LU factorization on GPU tensor cores: reducing data movement and memory footprint

Mixed precision LU factorization on GPU tensor cores: reducing data movement and memory footprint

AREND: A Faster and Robust Solution for Dynamic LR and QR Factorization

Exact QR factorizations of rectangular matrices

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