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A Universal Methodology of Complex Number Computation for Low-Complexity and high-Speed Implementation

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2025年第3期72卷 1308-1320页

作者： Wang, Yu Zhang, Jin Wu, Youlong Lyu, Fei Luo, Yuanyong Nanjing Xiaozhuang Univ Sch Elect Engn Nanjing 211171 Peoples R China Jinling Inst Technol Sch Elect & Informat Engn Nanjing 211169 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Integrated Circuits Nanjing 211106 Peoples R China Nanjing Univ Sch Phys Nanjing 210093 Peoples R China Huawei Corp Dept Turing Architecture Design Linx Lab HiSilicon Shenzhen 518129 Peoples R China

In complex-valued neural network (CVNN) applications, complex number calculations require high performance rather than high precision. However, most previous studies focused on high-precision approaches, which have low speed and high hardware costs. This paper proposes a universal methodology of complex number computation for low-complexity and high-speed implementation. The proposed methodology is based on the piecewise linear (PWL) method and can be used for different types of complex number computations. Considering that multiplication operations consume considerable resources, multiplication, fused square-add (FSA) and fused multiply-add (FMA) operations are the focus of optimization. The partial products of the square operation are reduced by folding and merging techniques because of their symmetry in the FSA operation. The partial products of the multiplication and FMA operations are reduced via Booth encoding. In addition, the partial products are further reduced by the proposed step-by-step truncation method. The proposed segmenter, which simulates the hardware implementation, automatically divides the nonlinear functions in the complex number computations into the smallest number of segments according to the required precision. The results show that the proposed approach improves performance and reduces hardware costs compared with the state-of-the-art methods for complex number calculations involving square roots, reciprocals and logarithms.

关键词： Hardware Image segmentation software Neural networks Costs Signal processing algorithms Power demand optimization Merging Encoding Piecewise linear (PWL) approximation method computation for complex numbers step-by-step truncation square root calculation of complex numbers reciprocal calculation of complex numbers logarithm calculation of complex numbers

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A data-driven TSK fuzzy system with adaptive rule construction for high-dimensional regression problems 2

A data-driven TSK fuzzy system with adaptive rule constructi...

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2nd International conference on Big Data, Computational Intelligence, and Applications, BDCIA 2024

作者： Yan, Yuxin City University of Macau Taipa China

ISBN: (纸本)9781510689053

high-dimensional functional regression problems are important topics in the field of complex system modeling and prediction. However, traditional machine learning algorithms often struggle to effectively handle high-dimensional input spaces and nonlinear mapping relationships, resulting in poor model performance and computational efficiency. To address this challenge, this paper proposes an innovative regression modeling approach based on fuzzy logic. This method cleverly utilizes the advantages of fuzzy logic to achieve nonlinear mapping from high-dimensional inputs to outputs through data-driven fuzzy rule base construction and efficient fuzzy inference mechanisms. In the rule base construction phase, we use fuzzy partitioning and clustering algorithms to automatically extract a compact set of rules. In the inference phase, we employ a computationally efficient TSK (Takagi-Sugeno-Kang) inference mechanism and parameter learning algorithm to achieve adaptive optimization of model performance. Extensive experiments demonstrate that the proposed fuzzy logic regression model significantly outperforms traditional machine learning algorithms in terms of regression performance and computational efficiency, exhibiting excellent generalization capability and robustness. Furthermore, through parameter sensitivity analysis, we reveal the inherent connections between model performance and key factors, providing important insights for practical applications. The research findings of this paper provide a novel and effective solution for high-dimensional functional regression problems, which is expected to advance the development of complex system modeling and prediction technologies. © 2025 SPIE.

关键词： Fuzzy inference

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PEbfs: Implement high-performance Breadth-First Search on PEZY-SC3s 24th

PEbfs: Implement High-Performance Breadth-First Search on P...

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24th International conference on algorithms and Architectures for Parallel Processing, ICA3PP 2024

作者： Guo, Weihao Wang, Qinglin Liu, Xiaodong Peng, Muchun Yang, Shun Liang, Yaling Shi, Yongzhen Cao, Ligang Liu, Jie Laboratory of Digitizing Software for Frontier Equipment National University of Defense Technology Changsha410073 China National Key Laboratory of Parallel and Distributed Computing National University of Defense Technology Changsha410073 China Engineering Research Center for National Fundamental Software National University of Defense Technology Changsha410073 China

ISBN: (纸本)9789819615506

The breadth-first search (BFS) algorithm is a fundamental algorithm in graph theory, and it’s parallelization can significantly improve performance. Therefore, there have been numerous efforts to leverage the powerful parallel computing capabilities of hardware like GPGPU to implement high-performance BFS algorithms. However, the energy efficiency is relatively low due to the high power consumption of the platforms on which the algorithm is adapted to. To deal with these challenges, this paper introduces PEbfs that is a high-performance BFS algorithm based on the PEZY-SC3s efficient processor. We integrated three search algorithms, two algorithm optimization strategies, and a directional optimization scheme into PEbfs. Through multiple evaluations of the performance of PEbfs on the public SNAP dataset, the results demonstrate that the average energy efficiency ratio of PEbfs is higher than that of Enterprise and Tigr, the two most advanced implementations on Nvidia’s GPGPU: It achieves 3.08× the average energy efficiency ratio of Enterprise and 4.53× that of Tigr. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： optimization algorithms

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An Improved Modified Jaya optimization Algorithm: Application to the Solution of nonlinear Equation Systems 4th

An Improved Modified Jaya Optimization Algorithm: Applicatio...

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

作者： Silva, Bruno Guerreiro Lopes, Luiz Doctoral Program in Informatics Engineering University of Madeira Madeira Island Funchal Portugal Regional Secretariat for Education Science and Technology Regional Government of Madeira Funchal Portugal Faculty of Exact Sciences and Engineering University of Madeira Madeira Island Funchal9020-105 Portugal

ISBN: (纸本)9783031812408

Population-based metaheuristic algorithms have been used to solve challenging optimization problems, and numerous modifications to make these algorithms more efficient have been proposed. Jaya is one of these algorithms that has been modified and utilized to solve many hard optimization problems. One such modification to the original algorithm is the Modified Jaya (MJAYA) algorithm, which, like Jaya, uses information about the best and worst candidate solutions to determine the population’s search direction, thereby limiting and focusing the search. Recent research has demonstrated that the MJAYA algorithm is not effective at solving systems of nonlinear equations transformed into equivalent nonlinear optimization problems. Systems of nonlinear equations are probably the most difficult class of numerical mathematics problems to solve, which justifies the use of metaheuristic approaches in their resolution. This paper proposes a new population-based optimization algorithm, the Improved Modified Jaya (IM-Jaya) algorithm, which, despite being a generic metaheuristic optimization algorithm, is here used to solve systems of nonlinear equations. The proposed algorithm strikes a better balance between global exploration and local exploitation, allowing for a broader and more exhaustive exploration of the search space as well as a more efficient local search in its most promising regions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： optimization algorithms

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GPU Acceleration of the Enhanced Jaya optimization Algorithm for Solving Large Systems of nonlinear Equations 4th

GPU Acceleration of the Enhanced Jaya Optimization Algorit...

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

ISBN: (纸本)9783031812408

This paper presents a GPU-based parallel implementation of the Enhanced Jaya (EJAYA) algorithm for solving large-scale systems of nonlinear equations. EJAYA is a gradient-free metaheuristic optimization scheme based on the population-based parameter-less Jaya algorithm that has recently been shown to be capable of solving nonlinear equation systems, a class of challenging problems that are difficult to solve by traditional approaches, particularly as systems become larger. The proposed parallel algorithm was implemented using the Julia programming language on a high-performance GeForce RTX 3090 GPU with 10 496 CUDA cores and 24 GB GDDR6X VRAM and was tested using a set of difficult scalable nonlinear equation system problems. The obtained results, with average speedups up to 122.25x, evidenced the capability of the proposed GPU-based parallel algorithm to meet the computational demands of the important class of problems under consideration. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： optimization algorithms

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An Improved Multi-objective Grey Wolf optimization Algorithm and its Application to the Optimal Design of Electromagnetic Devices 19th

An Improved Multi-objective Grey Wolf Optimization Algorithm...

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19th Annual conference of China Electrotechnical Society, ACCES 2024

作者： Wang, Xinyu Li, Yilun College of Information Science and Technology Donghua University Shanghai201620 China

ISBN: (纸本)9789819646746

As society advances and science and technology progress continuously, the requirements for electrical equipment have become increasingly stringent. Among these challenges, the optimization design of electromagnetic devices poses a complex multi-objective optimization problem due to the existence of coupled physical fields and the involvement of multiple conflicting objectives. Evolutionary-based optimization algorithms are widely employed to address such issues because of their practicality and effectiveness. However, many algorithms are prone to falling into local optima and exhibit poor stability when dealing with complex, high-dimensional, nonlinear mathematical programming problems. To address these issues, an improved multi-objective grey wolf optimization algorithm is proposed. In the improved algorithm, a good point set strategy is utilized in the population initialization;a nonlinear convergence factor is adopted to balance the algorithm’s optimization speed and accuracy;the Levy flight strategy is introduced to effectively utilize the search space, and the population updating mechanism in the beluga whale algorithm’s whale-fall behavior is introduced to further enhance the global search ability. The performance of the proposed algorithm is verified by means of the ZDT series test functions and is applied to the optimal design of a typical electromagnetic device. The numerical results manifest its accuracy and effectiveness. © Beijing Paike Culture Commu. Co., Ltd. 2025.

关键词： Multiobjective optimization

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Target Tracking Technology based on Improved Swarm Intelligent Particle Filter via PauTa Criterion Migration optimization 16

Target Tracking Technology based on Improved Swarm Intellige...

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16th International conference on Signal Processing Systems, ICSPS 2024

作者： Wang, Xihao Chen, Die School of Mathematical Sciences University of Electronic Science and Technology of China Chengdu China

ISBN: (纸本)9781510689251

Particle filter (PF) has been confirmed to be an effective method for nonlinear non-Gaussian systems. However, it is difficult to calculate the importance density function and particle degradation (particle simplification) is prone to occur. For the importance density function selection problem, an improved echolocation algorithm is used to approximate the optimal importance density function and optimize the particle distribution to make it closer to the high-likelihood region. For the problem of resampling, an improved dolphin swarm optimization algorithm has been developed to replace traditional resampling methods, which enhances the diversity of particles and further optimizes particle distribution, thereby improving the estimation accuracy. From the perspective of probability statistics, it proposes a "PauTa Criterion" optimization strategy suitable for various types of particle filter algorithms. This method migrates particles regarded as "impossible" in probability to optimize the particle distribution directly. Simulation experiments show that the " PauTa Criterion " optimization strategy has a good optimization effect on particle filter-based algorithms. The improved methods for both importance density and resampling exhibit excellent estimation performance, which improves the estimation accuracy of the PF and reduces its dependence on the number of particles. © 2025 SPIE.

关键词： Dolphins (structures)

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

4th International Conference on Numerical Computations: Theo...

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

ISBN: (纸本)9783031812460

The proceedings contain 105 papers. The special focus in this conference is on Numerical Computations: Theory and algorithms. The topics include: Resource Allocation via Bayesian optimization: an Efficient Alternative to Semi-Bandit Feedback;multi-Objective and Multiple Information Source optimization for Fair & Green Machine Learning;extended Optimal Control Problem for Practical Application;explainable Process Deviance Discovery with Data-Efficient Deep Learning;line Search Stochastic Gradient Algorithm with A-priori Rule for Monitoring the Control of the Variance;a Machine Learning Approach to Speed up the Solution of the Distributor’s Pallet Loading Problem;combined First- and Second-Order Directions for Deep Neural Networks Training;constrained Global optimization by Smoothing;the Unreasonable Effectiveness of Optimal Transport Distance in the Design of Multi-Objective Evolutionary optimization algorithms;an Improved Modified Jaya optimization Algorithm: Application to the Solution of nonlinear Equation Systems;GPU Acceleration of the Enhanced Jaya optimization Algorithm for Solving Large Systems of nonlinear Equations;effective Resistance Based Community Detection in Complex Networks;a Comparison of Formulations for Aircraft Deconfliction;optimal Recombination Problem in Genetic Programming for Boolean Functions;heuristics with Local Improvements for Two-Processor Scheduling Problem with Energy Constraint and Parallelization;numerical Analysis of Optimal Control of Assets and Liabilities by a Bank;optimal Control for Stochastic Multi-agent Systems With the Use of Parallel Hybrid Genetic Algorithm;DC optimization in Adversarial Sparse Support Vector Machine;A First-Order Optimality Condition in Nonsmooth Generalized Semi-infinite Programming (GSIP);miniaturisation of Binary Classifiers Through Sparse Neural Networks;Price Forecasting for Bitcoin: Linear Regression and SVM Approaches;inside the Box: 0–1 Linear Programming Under Interval Uncertainty;machine Learn

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

4th International Conference on Numerical Computations: Theo...

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

ISBN: (纸本)9783031812408

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

4th International Conference on Numerical Computations: Theo...

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4th International conference on Numerical Computations: Theory and algorithms, NUMTA 2023

ISBN: (纸本)9783031812439

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