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Ocean bottom seismograph relocation and time correction using the MCMC algorithm 认领 引用 被引量：1
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作者 Hao Hu Xiongwei Niu +6 位作者 Wei Wang Wencai Xu Aiguo Ruan Wenfei Gong Xiaodong Wei Mingju Xu Tao Li 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2025年第10期101-111,共11页
The ocean bottom seismograph(OBS)is a powerful device deployed on the seafloor for acquiring marine seismic data,capable of detecting the multi-scale Earth’s interiors from submarine sediments to the mantle.Due to th... The ocean bottom seismograph(OBS)is a powerful device deployed on the seafloor for acquiring marine seismic data,capable of detecting the multi-scale Earth’s interiors from submarine sediments to the mantle.Due to the frequent use of free-fall deployment,it is challenging to accurately track its precise position.Additionally,the internal crystal oscillator clock of the OBS has limited accuracy,resulting in clock drift for long-term work on the seabed.To improve the reliability of OBS detections,it is crucial to calculate the precise OBS location and time correction.Focusing on accurately determining OBS position and timing,this study developed a positioning method that integrates time correction based on the Markov Chain Monte Carlo(MCMC)algorithm,utilizing travel times of direct water waves triggered by two-dimensional(2-D)shot lines or three-dimensional(3-D)airgun arrays.This newly developed method can simultaneously estimate accurate OBS location and time correction,incorporating bathymetric data into the inversion procedures to improve sampling efficiency and enhance the reliability of the final results.Synthetic tests with appropriate noise levels are performed independently to evaluate the feasibility and reliability of our method,indicating that it is robust enough to determine OBS location and time correction precisely.Finally,we use travel-time data recorded at three OBSs deployed in the Southwest Indian Ridge to relocate locations and calculate time corrections.The results exhibit high consistency when using 2-D and 3-D shot data,indicating that high-resolution bathymetric data plays a fingerprint role in inversion to evaluate precise OBS location and time correction. 展开更多
关键词 ocean bottom seismograph positioning time correction marine seismic data acquisition Metropolis-Hastings algorithm marine seismic observation
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Adaptive Time Synchronization in Time Sensitive-Wireless Sensor Networks Based on Stochastic Gradient Algorithms Framework 认领 引用 被引量：2
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作者 Ramadan Abdul-Rashid Mohd Amiruddin Abd Rahman +1 位作者 Kar Tim Chan Arun Kumar Sangaiah 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第3期2585-2616,共32页
This study proposes a novel time-synchronization protocol inspired by stochastic gradient algorithms.The clock model of each network node in this synchronizer is configured as a generic adaptive filter where different... This study proposes a novel time-synchronization protocol inspired by stochastic gradient algorithms.The clock model of each network node in this synchronizer is configured as a generic adaptive filter where different stochastic gradient algorithms can be adopted for adaptive clock frequency adjustments.The study analyzes the pairwise synchronization behavior of the protocol and proves the generalized convergence of the synchronization error and clock frequency.A novel closed-form expression is also derived for a generalized asymptotic error variance steady state.Steady and convergence analyses are then presented for the synchronization,with frequency adaptations done using least mean square(LMS),the Newton search,the gradient descent(GraDes),the normalized LMS(N-LMS),and the Sign-Data LMS algorithms.Results obtained from real-time experiments showed a better performance of our protocols as compared to the Average Proportional-Integral Synchronization Protocol(AvgPISync)regarding the impact of quantization error on synchronization accuracy,precision,and convergence time.This generalized approach to time synchronization allows flexibility in selecting a suitable protocol for different wireless sensor network applications. 展开更多
关键词 Wireless sensor network time synchronization stochastic gradient algorithm multi-hop
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Probabilistic Assessment of PV-DG for Optimal Multi-Locations and Sizing Using Genetic Algorithm and Sequential-Time Power Flow 认领 引用
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作者 A. Elkholy 《Journal of Power and Energy Engineering》 2025年第2期23-42,共20页
This paper presents an optimized strategy for multiple integrations of photovoltaic distributed generation (PV-DG) within radial distribution power systems. The proposed methodology focuses on identifying the optimal ... This paper presents an optimized strategy for multiple integrations of photovoltaic distributed generation (PV-DG) within radial distribution power systems. The proposed methodology focuses on identifying the optimal allocation and sizing of multiple PV-DG units to minimize power losses using a probabilistic PV model and time-series power flow analysis. Addressing the uncertainties in PV output due to weather variability and diurnal cycles is critical. A probabilistic assessment offers a more robust analysis of DG integration’s impact on the grid, potentially leading to more reliable system planning. The presented approach employs a genetic algorithm (GA) and a determined PV output profile and probabilistic PV generation profile based on experimental measurements for one year of solar radiation in Cairo, Egypt. The proposed algorithms are validated using a co-simulation framework that integrates MATLAB and OpenDSS, enabling analysis on a 33-bus test system. This framework can act as a guideline for creating other co-simulation algorithms to enhance computing platforms for contemporary modern distribution systems within smart grids concept. The paper presents comparisons with previous research studies and various interesting findings such as the considered hours for developing the probabilistic model presents different results. 展开更多
关键词 Photovoltaic Distributed Generation Probability Genetic Algorithm Radial Distribution Systems Time Series Power Flow
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Phase matching sampling algorithm for sampling rate reduction in time division multiplexing optical fiber sensor system 认领 引用
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作者 Junhui Wu Zhilin Xu +2 位作者 Yi Shi Yurong Liang Qizhen Sun 《Opto-Electronic Technology》 2025年第2期51-63,共13页
Time division multiplexing(TDM)architecture is an important approach to creating sensor arrays for massive scale monitoring.But it is paradoxical for the TDM interferometric sensor array to keep a short delay fiber fo... Time division multiplexing(TDM)architecture is an important approach to creating sensor arrays for massive scale monitoring.But it is paradoxical for the TDM interferometric sensor array to keep a short delay fiber for high sensing resolution and meanwhile use low sampling rate for practical applications.In this paper,a phase matching sampling(PMS)paradigm is proposed to address the above contradiction.By matching the phase of the sampling clock with the delay fiber length,combining with multiple-pulses sampling strategy,the proposed PMS method can avoid collecting the redundant information,facilitating the decreasing of sampling rate as well as delay fiber length of the TDM sensing system.The proof-of-concept experiments on an 8-channel TDM interferometric system demonstrate that when the sampling rate is fixed at 20 MS/s,by applying the PMS algorithm,the delay fiber length can be shortened from 100 m to 1 m,compared with applying the conventional sampling method.It reduced the phase noise of the system by a factor of 10 at 1 mHz and by a factor of 50 at 1 Hz.The PMS algorithm for greatly reducing the sampling rate is expected to fuel the TDM interferometric sensor arrays for many applications. 展开更多
关键词 time division multiplexing system sampling algorithm interferometric fiber optic sensors displacement sensing array
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Scheduling algorithm of dual-armed cluster tools with residency time and reentrant constraints 认领 引用 被引量：8
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作者 周炳海 高忠顺 陈佳 《Journal of Central South University》 SCIE EI CAS 2014年第1期160-166,共7页
To solve the scheduling problem of dual-armed cluster tools for wafer fabrications with residency time and reentrant constraints,a heuristic scheduling algorithm was developed.Firstly,on the basis of formulating sched... To solve the scheduling problem of dual-armed cluster tools for wafer fabrications with residency time and reentrant constraints,a heuristic scheduling algorithm was developed.Firstly,on the basis of formulating scheduling problems domain of dual-armed cluster tools,a non-integer programming model was set up with a minimizing objective function of the makespan.Combining characteristics of residency time and reentrant constraints,a scheduling algorithm of searching the optimal operation path of dual-armed transport module was presented under many kinds of robotic scheduling paths for dual-armed cluster tools.Finally,the experiments were designed to evaluate the proposed algorithm.The results show that the proposed algorithm is feasible and efficient for obtaining an optimal scheduling solution of dual-armed cluster tools with residency time and reentrant constraints. 展开更多
关键词 dual-armed cluster tools scheduling residency time constraints reentrancy heuristic algorithm
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A Discrete Artificial Bee Colony Algorithm for Minimizing the Total Flow Time in the Blocking Flow Shop Scheduling 认领 引用 被引量：11
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作者 邓冠龙 徐震浩 顾幸生 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2012年第6期1067-1073,共7页
A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Se... A discrete artificial bee colony algorithm is proposed for solving the blocking flow shop scheduling problem with total flow time criterion. Firstly, the solution in the algorithm is represented as job permutation. Secondly, an initialization scheme based on a variant of the NEH (Nawaz-Enscore-Ham) heuristic and a local search is designed to construct the initial population with both quality and diversity. Thirdly, based on the idea of iterated greedy algorithm, some newly designed schemes for employed bee, onlooker bee and scout bee are presented. The performance of the proposed algorithm is tested on the well-known Taillard benchmark set, and the computational results demonstrate the effectiveness of the discrete artificial bee colony algorithm. In addition, the best known solutions of the benchmark set are provided for the blocking flow shop scheduling problem with total flow time criterion. 展开更多
关键词 blocking flow shop scheduling artificial bee colony algorithm total flow time
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Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform 认领 引用 被引量：8
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作者 Bian Hailong Chen Guangju 《Journal of Systems Engineering and Electronics》 SCIE EI 2008年第3期419-426,共8页
To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals,a novel kind of anti-aliasing algorithm based on the short time Fourier transform(STFT)is brought forward.First ... To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals,a novel kind of anti-aliasing algorithm based on the short time Fourier transform(STFT)is brought forward.First the physical essence of aliasing that occurs is analyzed;second the interpolation algorithm model is setup based on the Hamming window;then the fast implementation of the algorithm using the Newton iteration method is given.Using the numerical simulation the feasibility of algorithm is validated.Finally,the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering. 展开更多
关键词 nonstationary signal interpolation anti-aliasing short time Fourier transform(STFT) iterative algorithm.
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Application of Bat Algorithm Based Time Optimal Control in Multi-robots Formation Reconfiguration 认领 引用 被引量：2
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作者 Guannan Li Hongli Xu Yang Lin 《Journal of Bionic Engineering》 SCIE EI CSCD 2018年第1期126-138,共13页
This paper proposes a Bat Algorithm （BA） based Control Parameterization and Time Discretization （BA-CPTD） method to acquire time optimal control law for formation reconfiguration of multi-robots system. In this me... This paper proposes a Bat Algorithm （BA） based Control Parameterization and Time Discretization （BA-CPTD） method to acquire time optimal control law for formation reconfiguration of multi-robots system. In this method, the problem of seeking for time optimal control law is converted into a parameter optimization problem by control parameterization and time discretization, so that the control law can be derived with BA. The actual state of a multi-robots system is then introduced as feedback information to eliminate formation error. This method can cope with the situations where the accurate mathematical model of a system is unavailable or the disturbance from the environment exists. Field experiments have verified the effectiveness of the proposed method and shown that formation converges faster than some existing methods. Further experiment results illustrate that the time optimal control law is able to provide smooth control input for robots to follow, so that the desired formation can be attained rapidly with minor formation error. The formation error will finally be eliminated by using actual state as feedback. 展开更多
关键词 Bat Algorithm CPTD method multi-robots formation control time optimal control
Prediction of Time Series Empowered with a Novel SREKRLS Algorithm 认领 引用 被引量：3
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作者 Bilal Shoaib Yasir Javed +6 位作者 Muhammad Adnan Khan Fahad Ahmad Rizwan Majeed Muhammad Saqib Nawaz Muhammad Adeel Ashraf Abid Iqbal Muhammad Idrees 《Computers, Materials & Continua》 SCIE EI 2021年第5期1413-1427,共15页
For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself ... For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm. 展开更多
关键词 Kernel methods square root adaptive filtering givens rotation mackey glass time series prediction recursive least squares kernel recursive least squares extended kernel recursive least squares square root extended kernel recursive least squares algorithm
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Solving open vehicle problem with time window by hybrid column generation algorithm 认领 引用 被引量：1
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作者 YU Naikang QIAN Bin +2 位作者 HU Rong CHEN Yuwang WANG Ling 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2022年第4期997-1009,共13页
This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the ... This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process.We propose a hybrid column generation algorithm(HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time. 展开更多
关键词 open vehicle routing problem with time window(OVRPTW) hybrid column generation algorithm(HCGA) mixed integer programming label setting algorithm
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Stabilization of Chaotic Time Series by Proportional Pulse in the System Variable Based on Genetic Algorithm 认领 引用 被引量：1
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作者 Qing Li Deling Zheng Jianlong Zhou 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS 1999年第3期228-229,共2页
The PPSV(Proportional Pulse in the System Variable)algorithm is a convenient method for the stabilization of the chaotic time series.It does not require any previous knowledge of the system.The PPSV method also has a ... The PPSV(Proportional Pulse in the System Variable)algorithm is a convenient method for the stabilization of the chaotic time series.It does not require any previous knowledge of the system.The PPSV method also has a shortcoming,that is,the determination off.is a procedure by trial and error,since it lacks of optimization.In order to overcome the blindness,GA(Genetic Algorithm),a search algorithm based on the mechanics of natural selection and natural genetics,is used to optimize theλi The new method is named as GAPPSV algorithm.The simulation results show that GAPPSV algorithm is very efficient because the control process is short and the steady-state error is small. 展开更多
关键词 stabilization chaotic time series genetic algorithm
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An Improved Higher-Order Time Integration Algorithm for Structural Dynamics 认领 引用 被引量：1
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作者 Yi Ji Yufeng Xing 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第2期549-575,共27页
Based on the weighted residual method,a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed,which is superior to the second-order accurate algorithms in trac... Based on the weighted residual method,a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed,which is superior to the second-order accurate algorithms in tracking long-term dynamics.For improving such a higher-order accurate algorithm,this paper proposes a two sub-step higher-order algorithm with unconditional stability and controllable dissipation.In the proposed algorithm,a time step interval[tk,tk+h]where h stands for the size of a time step is divided into two sub-steps[tk,tk+γh]and[tk+γh,tk+h].A non-dissipative fourth-order algorithm is used in the rst sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to lter out the contribution of high-frequency modes.Besides,two approaches are used to design the algorithm parameterγ.The rst approach determinesγby maximizing low-frequency accuracy and the other determinesγfor quickly damping out highfrequency modes.The present algorithm usesρ∞to exactly control the degree of numerical dissipation,and it is third-order accurate when 0≤ρ∞<1 and fourth-order accurate whenρ∞=1.Furthermore,the proposed algorithm is self-starting and easy to implement.Some illustrative linear and nonlinear examples are solved to check the performances of the proposed two sub-step higher-order algorithm. 展开更多
关键词 Time integration algorithm two-sub-step higher-order accuracy controllable dissipation unconditional stability
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Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times 认领 引用 被引量：1
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作者 Li Kai Yang Shanlin 《Journal of Systems Engineering and Electronics》 SCIE EI 2008年第4期827-834,共8页
A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time.Models and relaxations are collected.Most of these problems are NP-hard,i... A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time.Models and relaxations are collected.Most of these problems are NP-hard,in the strong sense,or open problems,therefore approximation algorithms are studied.The review reveals that there exist some potential areas worthy of further research. 展开更多
关键词 parallel machine scheduling review total weighted completion time relaxation algorithm
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A hybrid algorithm based on ILP and genetic algorithm for time-aware test case prioritization 认领 引用 被引量：1
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作者 Sun Jiaze Wang Gang 《Journal of Southeast University(English Edition)》 EI CAS 2018年第1期28-35,共8页
To solve the problem of time-awarc test case prioritization,a hybrid algorithm composed of integer linear programming and the genetic algorithm(ILP-GA)is proposed.First,the test case suite which cm maximize the number... To solve the problem of time-awarc test case prioritization,a hybrid algorithm composed of integer linear programming and the genetic algorithm(ILP-GA)is proposed.First,the test case suite which cm maximize the number of covered program entities a d satisfy time constraints is selected by integer linea progamming.Secondly,the individual is encoded according to the cover matrices of entities,and the coverage rate of program entities is used as the fitness function and the genetic algorithm is used to prioritize the selected test cases.Five typical open source projects are selected as benchmark programs.Branch and method are selected as program entities,and time constraint percentages a e 25%and 75%.The experimental results show that the ILP-GA convergence has faster speed and better stability than ILP-additional and IP-total in most cases,which contributes to the detection of software defects as early as possible and reduces the software testing costs. 展开更多
关键词 test case prioritization integer linear programming(I LP) genetic algorithm time constraint
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A novel genetic algorithm for vehicle routing problem with time windows 认领 引用 被引量：2
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作者 刘云忠 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第3期437-444,共8页
A novel genetic algorithm with multiple species in dynamic region is proposed,each of which occupies a dynamic region determined by the weight vector of a fuzzy adaptive Hamming neural network. Through learning and cl... A novel genetic algorithm with multiple species in dynamic region is proposed,each of which occupies a dynamic region determined by the weight vector of a fuzzy adaptive Hamming neural network. Through learning and classification of genetic individuals in the evolutionary procedure,the neural network distributes multiple species into different regions of the search space. Furthermore,the neural network dynamically expands each search region or establishes new region for good offspring individuals to continuously keep the diversification of the genetic population. As a result,the premature problem inherent in genetic algorithm is alleviated and better tradeoff between the ability of exploration and exploitation can be obtained. The experimental results on the vehicle routing problem with time windows also show the good performance of the proposed genetic algorithm. 展开更多
关键词 genetic algorithm multiple species neural network premature problem vehicle routing problem with time windows
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Modeling of Borehole Radar for Well Logging Using Pseudo-spectral Time Domain Algorithm 认领 引用 被引量：2
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作者 林树海 《Journal of Earth Science》 SCIE CAS 2009年第6期978-984,共7页
In this article, numerical modeling of borehole radar for well logging in time domain is developed using pseudo-spectral time domain algorithm in axisymmetric cylindrical coordinate for proximate true formation model.... In this article, numerical modeling of borehole radar for well logging in time domain is developed using pseudo-spectral time domain algorithm in axisymmetric cylindrical coordinate for proximate true formation model. The conductivity and relative permittivity logging curves are obtained from the data of borehole radar for well logging. Since the relative permittivity logging curve is not affected by salinity of formation water, borehole radar for well logging has obvious advantages as compared with conventional electrical logging. The borehole radar for well logging is a one-transmitter and two-receiver logging tool. The conductivity and relative permittivity logging curves are obtained successfully by measuring the amplitude radio and the time difference of pulse waveform from two receivers. The calculated conductivity and relative permittivity logging curves are close to the true value of surrounding formation, which tests the usability and reliability of borehole radar for well logging. The numerical modeling of borehole radar for well logging laid the important foundation for researching its logging tool. 展开更多
关键词 borehole radar well logging pseudo-spectral time domain algorithm conductivity permittivity.
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Positioning performance analysis of the time sum of arrival algorithm with error features 认领 引用 被引量：1
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作者 宫峰勋 马艳秋 《Optoelectronics Letters》 EI 2018年第2期133-137,共5页
The theoretical positioning accuracy of multilateration(MLAT) with the time difference of arrival(TDOA) algorithm is very high. However, there are some problems in practical applications. Here we analyze the location ... The theoretical positioning accuracy of multilateration(MLAT) with the time difference of arrival(TDOA) algorithm is very high. However, there are some problems in practical applications. Here we analyze the location performance of the time sum of arrival(TSOA) algorithm from the root mean square error(RMSE) and geometric dilution of precision(GDOP) in additive white Gaussian noise(AWGN) environment. The TSOA localization model is constructed. Using it, the distribution of location ambiguity region is presented with 4-base stations. And then, the location performance analysis is started from the 4-base stations with calculating the RMSE and GDOP variation. Subsequently, when the location parameters are changed in number of base stations, base station layout and so on, the performance changing patterns of the TSOA location algorithm are shown. So, the TSOA location characteristics and performance are revealed. From the RMSE and GDOP state changing trend, the anti-noise performance and robustness of the TSOA localization algorithm are proved. The TSOA anti-noise performance will be used for reducing the blind-zone and the false location rate of MLAT systems. 展开更多
关键词 Positioning performance analysis of the time sum of arrival algorithm with error features
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Self-learning Fuzzy Controllers Based On a Real-time Reinforcement Genetic Algorithm 认领 引用
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作者 方建安 苗清影 +1 位作者 郭钊侠 邵世煌 《Journal of Donghua University(English Edition)》 EI CAS 2002年第2期19-22,共4页
This paper presents a novel method for constructing fuzzy controllers based on a real time reinforcement genetic algorithm. This methodology introduces the real-time learning capability of neural networks into globall... This paper presents a novel method for constructing fuzzy controllers based on a real time reinforcement genetic algorithm. This methodology introduces the real-time learning capability of neural networks into globally searching process of genetic algorithm, aiming to enhance the convergence rate and real-time learning ability of genetic algorithm, which is then used to construct fuzzy controllers for complex dynamic systems without any knowledge about system dynamics and prior control experience. The cart-pole system is employed as a test bed to demonstrate the effectiveness of the proposed control scheme, and the robustness of the acquired fuzzy controller with comparable result. 展开更多
关键词 fuzzy controller, self-learning, real time,reinforcement, genetic algorithm
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A new escape time algorithm of constructing Julia set 认领 引用
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作者 袁杰 Li Xiali +1 位作者 Hou Zhiling Cao Maosheng 《High Technology Letters》 EI CAS 2007年第2期194-197,共4页
Escape time algorithm is an effective theoretical algorithm of constructing fractal graphics. The key of this algorithm lies in the construction of escape time function. A new escape time function is presented based o... Escape time algorithm is an effective theoretical algorithm of constructing fractal graphics. The key of this algorithm lies in the construction of escape time function. A new escape time function is presented based on the research of escape time algorithm. An accelerated escape time algorithm is carried out in this paper. The experiments have demonstrated that the new algorithm is not only as precise as the old, but also faster when it is used to construct Julia set. 展开更多
关键词 fractal escape time algorithm escape time function Julia set
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Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems 认领 引用
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作者 Chein-Shan Liu Jian-Hung Shen +1 位作者 Chung-Lun Kuo Yung-Wei Chen 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1317-1335,共19页
This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve... This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency. 展开更多
关键词 Nonlinear eigenvalue problem quadratic eigenvalue problem two new merit functions golden section search algorithm fictitious time integration method
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