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Structure and Principles of Operation of a Quaternion VLSI Multiplier

APPLIED SCIENCES-BASEL 2024年第18期14卷 8123页

作者： Cariow, Aleksandr Naumowicz, Mariusz Handkiewicz, Andrzej West Pomeranian Univ Technol Fac Comp Sci & Informat Technol PL-70310 Szczecin Poland Poznan Univ Tech Fac Comp Ul Piotrowo 3a PL-60965 Poznan Poland Jacob Paradise Univ Fac Technol PL-66400 Gorzow Wielkopolski Poland

The paper presents the original structure of a processing unit for multiplying quaternions. The idea of organizing the device is based on the use of fast Hadamard transform blocks. The operation principles of such a device are described. Compared to direct quaternion multiplication, the developed algorithm significantly reduces the number of multiplication and addition operations. Hardware implementations of the developed structure, in FPGA and ASIC, are presented. The FPGA blocks were implemented in the Vivado environment. The ASICs were designed using 130nm technology. The developed scripts in VHDL are available in the GitHub repository.

关键词： hypercomplex numbers quaternion multiplier fast algorithm matrix-vector multiplication hardware implementation FPGA ASIC

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VCNPU: An algorithm-Hardware Co-Optimized Framework for Accelerating Neural Video Compression

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 2025年第4期33卷 1014-1027页

作者： Zhang, Siyu Mao, Wendong Wang, Zhongfeng Nanjing Univ Sch Elect Sci & Engn Nanjing 210023 Peoples R China Sun Yat Sen Univ Sch Integrated Circuits Shenzhen 518107 Peoples R China

Video compression is essential for storing and transmitting video content. Real-time decoding is indispensable for delivering a seamless user experience. Neural video compression (NVC) integrates traditional coding techniques with deep learning, resulting in impressive compression efficiency. However, the real-time deployment of advanced NVC models encounters challenges due to their high complexity and extensive off-chip memory access. This article presents a novel NVC accelerator, called video compression neural processing unit (VCNPU), via an algorithm-hardware co-design framework. First, at the algorithmic level, a reparameterizable video compression network (RepVCN) is proposed to aggregate multiscale features and boost video compression quality. RepVCN can be equivalently transformed into a streamlined structure without extra computations after training. Second, a mask-sharing pruning strategy is proposed to compress RepVCN in the fast transform domain. It effectively prevents the destruction of sparse patterns caused by model simplification, maintaining the model capacity. Third, at the hardware level, a reconfigurable sparse computing module is designed to flexibly support sparse fast convolutions and deconvolutions of the compact RepVCN. Besides, a hybrid layer fusion pipeline is advocated to reduce off-chip data communication caused by extensive motion and residual features. Finally, based on the joint optimization of computation and communication, our VCNPU is constructed to realize adaptive adjustments of various decoding qualities and is implemented under TSMC 28-nm CMOS technology. Extensive experiments demonstrate that our RepVCN provides superior coding quality over other video compression baselines. Meanwhile, our VCNPU achieves 6.7 x improvements in throughput, 2.9 x in area efficiency, and 4 x in energy efficiency compared to prior video processors.

关键词： Video compression Computational modeling Transforms Hardware Streaming media Optimization Decoding Real-time systems Memory management Feature extraction fast algorithm hardware accelerator neural video compression (NVC) pruning reparameterization

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A Simple and Efficient Finite Difference Method for the Tempered Nonlocal Laplacian

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JOURNAL OF SCIENTIFIC COMPUTING 2025年第1期103卷 1-24页

作者： Cui, Xuehong Du, Rui Hao, Zhaopeng Southeast Univ Sch Math Nanjing Peoples R China

For the tempered nonlocal Laplacian, an efficient and accurate numerical evaluation in multi-dimensions is challenging due to the nature of a singular integral. In this research, we present a new approximation using the generating function or multiplier approximation theory to discretize the multi-dimensional tempered nonlocal Laplacian defined by a hypersingular integral. We show that the approximation can uniformly achieve the convergence of the second order, independent of the operator parameters. Using the proposed approximation, we construct a simple and easy-to-implement finite difference scheme to solve elliptic and parabolic equations with the tempered nonlocal Laplacian. We provide the analysis for convergence and stability of the scheme for the elliptic and parabolic equations. We also present a fast algorithm with quasi-linear complexity of the scheme for computing the tempered operator. Several numerical examples demonstrate the accuracy and efficiency of our algorithm and verify our theory.

关键词： Tempered nonlocal Laplacian Finite difference method Convergence Stability fast algorithm

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Acceleration of Large-Scale Power System Analysis Including Phase-Domain Rotating Machine Models Using Partial Refactorization in Electromagnetic Transient Analysis

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ELECTRICAL ENGINEERING IN JAPAN 2025年第1期218卷

作者： Yonezawa, Rikido Kawasaki, Shoji Cent Res Inst Elect Power Ind CRIEPI Yokosuka Kanagawa Japan Meiji Univ Grad Sch Sci & Technol Dept Elect Engn Kawasaki Japan

One of the models for rotating machines, such as synchronous machines and induction machines, is the phase-domain model, which is characterized by formulating the circuit equations of the rotating machine in the phase domain and solving them simultaneously with the external system to which the rotating machine is connected. Although this model has excellent numerical stability and calculation accuracy, it requires refactorization of the subcircuit that includes the rotating machine at each calculation time step, which degrades the calculation speed. This paper describes the results of an attempt to improve the calculation speed when using the phase-domain model by using partial refactorization, which makes the refactorization process more efficient.

关键词： electromagnetic transient analysis fast algorithm partial refactorization phase domain synchronous generator model

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Collocation-based numerical simulation of multi-dimensional nonlinear time-fractional Schrödinger equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2025年 183卷 214-233页

作者： Huang, Rong Weng, Zhifeng Yuan, Jianhua Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China Huaqiao Univ Sch Math Sci Quanzhou 362021 Peoples R China Beijing Univ Posts & Telecommun Key Lab Math & Informat Networks Minist Educ Beijing 100876 Peoples R China

This paper introduces meshless and high-precision barycentric interpolation collocation methods, grounded in two well-established difference formulas, for solving the nonlinear time-fractional Schr & ouml;dinger equation. This equation is characterized by complexity arising from power-law nonlinearity and multi-scale time dependence. To enhance spatial accuracy, we utilize two meshless barycentric interpolation collocation methods that exhibit exponential convergence in the spatial domain. After discretizing the spatial variables, we discretize the Caputo derivative using both the classical L1 formula and a related fast algorithm that incorporates the sum-ofexponentials technique. The nonlinear term is addressed through an explicit scheme augmented with a second-order stabilization term. Consequently, we derive fully discrete schemes capable of numerically solving the equation. Furthermore, we undertake comprehensive consistency analyses of the semi-discretized schemes in the spatial dimension, along with analyses of the nonlinear fully discretized schemes, leveraging the approximation properties of the collocation methods. Our numerical simulations, encompassing one, two, and three dimensions, conclusively demonstrate the remarkable accuracy and efficiency of the proposed collocation methods. Moreover, by comparing the error with that of a traditional finite difference method, we showcase that our schemes offer superior accuracy while requiring fewer nodes, thereby emphasizing their advantageous characteristics.

关键词： Nonlinear time-fractional Schr & ouml dinger equation Barycentric interpolation collocation L1 scheme fast algorithm Error estimate

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An α-robust two-grid finite element method with nonuniform L2-1σ scheme for the semilinear Caputo-Hadamard time-fractional diffusion equations involving initial singularity

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APPLIED MATHEMATICS AND COMPUTATION 2025年 496卷

作者： Zeng, Yunhua Tan, Zhijun Sun Yat sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Sun Yat sen Univ Guangdong Prov Key Lab Computat Sci Guangzhou 510006 Peoples R China

Considering the initial singularity, a fully discrete two-grid finite element method (FEM) on nonuniform temporal meshes is constructed for the semilinear time-fractional variable coefficient diffusion equations (TF-VCDEs) with Caputo-Hadamard derivative. The nonuniform Llog,2-1 sigma formula and two-grid method are employed to discretize the time and space directions, respectively. Through strict theoretical proof, the alpha-robust stability and optimal L2-norm and H1- norm error analysis for the fully discrete FEM and the two-grid method are obtained, where the error bound does not blow up as alpha -> 1-. To reduce computational costs, a fast two-grid method is constructed by approximating the kernel function with an effective sum-of-exponentials (SOE) technique. Finally, the accuracy and effectiveness of the two-grid method and its associated fast algorithm are verified through two numerical examples.

关键词： Time-fractional Caputo-Hadamard derivative Variable coefficient diffusion equations alpha-robust Two-grid method fast algorithm Error estimate Nonuniform Llog,2-1 sigma formula

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TINA: TMVP-Initiated Novel Accelerator for Lightweight Ring-LWE-Based PQC

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 2024年第5期32卷 870-882页

作者： Bao, Tianyou He, Pengzhou Bai, Shi Xie, Jiafeng Villanova Univ Dept Elect & Comp Engn Villanova PA 19085 USA Florida Atlantic Univ Dept Math Sci Boca Raton FL 33431 USA

Postquantum cryptography (PQC) has recently garnered significant attention across various communities. Alongside the ongoing standardization process for general-purpose PQC algorithms by the National Institute of Standards and Technology (NIST), the research community is actively exploring the realm of lightweight PQC schemes. A ring-binary-learning-with-error (RBLWE)-based encryption scheme (RBLWE-ENC) is a promising lightweight PQC candidate suitable for Internet-of-Things (IoT) and edge computing applications. The parameters of the RBLWE-ENC, however, do not favor deploying typical fast algorithms, such as number-theoretic transform (NTT). In this article, therefore, we propose to design a Toeplitz matrix-vector product (TMVP)-initiated novel accelerator (TINA) for RBLWE-ENC. We innovatively used TMVP (a subquadratic-complexity fast algorithm for polynomial multiplication) to derive the significant arithmetic operation of RBLWE-ENC into a new form for high-performance operation. This novel formulation culminates in the development of a comprehensive accelerator known as TINA. Through implementation and comparative analysis, we demonstrate the efficiency gains achieved by our proposed accelerator. To the authors' best knowledge, this is the first report on the TMVP strategy-initiated RBLWE-ENC accelerator. The findings of this work are expected to provide valuable references in the ongoing advancement of lightweight PQC development.

关键词： fast algorithm hardware accelerator high performance lightweight postquantum cryptography (PQC) ring-binary-learning-with-errors (RBLWEs) Toeplitz matrix-vector product (TMVP)

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faster independent vector analysis with joint pairwise updates of demixing vectors

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ARTIFICIAL INTELLIGENCE REVIEW 2024年第2期58卷 1-18页

作者： Luo, Zhongqiang Guo, Ruiming Wang, Ling Sichuan Univ Sci & Engn Sch Automat & Informat Engn Yibin 644000 Peoples R China Sichuan Univ Sci & Engn Artificial Intelligence Key Lab Sichuan Prov Yibin 644000 Peoples R China

To achieve more efficient blind separation of multi-channel speech signals, this paper proposes a new algorithm for blind source separation(BSS) of sound sources using auxiliary function-based independent vector analysis (AuxIVA) with joint pairwise updates of demixing vectors. This algorithm is better than AuxIVA using iterative projection with adjustment (AuxIVA-IPA) when separating multiple sources. The IPA method jointly executes iterative projection (IP) and iterative source steering (ISS) to update and updates one row and one column of the separation matrix in each iteration. On this basis, IPA is extended to jointly execute IP2 and ISS2 for updating, which can update two rows and two columns of the separation matrix in each iteration. Accordingly, this proposed method is named by IPA2. Furthermore, it can optimize the same cost function as IPA while maintaining the same time complexity. Finally, the convolutional speech separation experiments are conducted to validate the effectiveness and efficiency of the proposed method. The experimental results corroborate that compared with the state-of-the-art IP, IP2, ISS, ISS2, and IPA used in AuxIVA, the IPA2 method acquires faster convergence speed and better separation performance, enabling the cost function to reach the convergence interval faster and maintaining good separation results.

关键词： Blind source separation Independent vector analysis Auxiliary function optimization fast algorithm

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Analysis of a meshless generalized finite difference method for the time-fractional diffusion-wave equation

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2024年 172卷 134-151页

作者： Qing, Lanyu Li, Xiaolin Chongqing Normal Univ Sch Math Sci Chongqing 400047 Peoples R China

In this paper, a generalized finite difference method (GFDM) is proposed and analyzed for meshless numerical solution of the time-fractional diffusion-wave equation. Two (3 - alpha)-order accurate temporal discretization schemes are presented by using the L1 formula and the original H2N2 or fast H2N2 formulas to discretize the time-fractional derivative of order alpha is an element of (1, 2). The stability of the temporal discretization schemes is analyzed. Then, the time-fractional diffusion-wave initial-boundary value problem is transformed into a series of time-independent integer-order boundary value problems, and discrete linear algebraic systems are built by the application of the GFDM. Accuracy analysis of the GFDM with both original H2N2 and fast H2N2 formulas is presented in theory, and numerical experimental results are provided to verify the theoretical results and the effectiveness of the proposed meshless method.

关键词： Time-fractional diffusion-wave equation Meshless collocation methods Generalized finite difference method fast algorithm Error analysis

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Unconditionally optimal H¹-norm error estimates of a fast and linearized Galerkin method for nonlinear subdiffusion equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2022年第0期107卷 70-81页

作者： Liu, Nan Qin, Hongyu Yang, Yin Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China Xiangtan Univ Hunan Natl Appl Math Ctr Sch Math & Computat Sci Hunan Key Lab Computat & Simulat Sci & Engn Xiangtan 411105 Hunan Peoples R China

In this paper, the unconditionally optimal H-1-norm error estimate for a two-step fast L1 scheme is considered for a nonlinear subdiffusion equation, which involves the considerations of both the initial singularity of the solution and the computational complexity to evaluate the Caputo derivative. For the fully discrete scheme, we use the fast L1 scheme developed in [28] to speed up the evaluation of the Caputo derivative on nonuniform time step, employ the Galerkin finite element (FE) method to discretize the spatial direction, and take the Newton linearized method to approximate the nonlinear term. While the theory of the L-2-norm error estimate is well studied, there are few works on the unconditional convergence of H-1-norm error estimate of the linearized Galerkin FE scheme for nonlinear subdiffusion equations. The main reason is that it requires to find a suitable test function in the FE space. To this end, we here respectively take the time-discrete operator and Laplace operator as the suitable test function in the FE space, and combine an improved discrete fractional Gronwall inequality to achieve the unconditional error estimate in H-1-norm. Numerical results are provided to demonstrate the theoretical results.

关键词： H-1-norm error estimate Unconditional convergence fast algorithm

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