In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
Linear minimum mean square error(MMSE)detection has been shown to achieve near-optimal performance for massive multiple-input multiple-output(MIMO)systems but inevitably involves complicated matrix inversion,which ent...Linear minimum mean square error(MMSE)detection has been shown to achieve near-optimal performance for massive multiple-input multiple-output(MIMO)systems but inevitably involves complicated matrix inversion,which entails high complexity.To avoid the exact matrix inversion,a considerable number of implicit and explicit approximate matrix inversion based detection methods is proposed.By combining the advantages of both the explicit and the implicit matrix inversion,this paper introduces a new low-complexity signal detection algorithm.Firstly,the relationship between implicit and explicit techniques is analyzed.Then,an enhanced Newton iteration method is introduced to realize an approximate MMSE detection for massive MIMO uplink systems.The proposed improved Newton iteration significantly reduces the complexity of conventional Newton iteration.However,its complexity is still high for higher iterations.Thus,it is applied only for first two iterations.For subsequent iterations,we propose a novel trace iterative method(TIM)based low-complexity algorithm,which has significantly lower complexity than higher Newton iterations.Convergence guarantees of the proposed detector are also provided.Numerical simulations verify that the proposed detector exhibits significant performance enhancement over recently reported iterative detectors and achieves close-to-MMSE performance while retaining the low-complexity advantage for systems with hundreds of antennas.展开更多
Cross iteration often exists in the computational process of the simulation models, especially for control models. There is a credibility defect tracing problem in the validation of models with cross iteration. In ord...Cross iteration often exists in the computational process of the simulation models, especially for control models. There is a credibility defect tracing problem in the validation of models with cross iteration. In order to resolve this problem, after the problem formulation, a validation theorem on the cross iteration is proposed, and the proof of the theorem is given under the cross iteration circumstance. Meanwhile, applying the proposed theorem, the credibility calculation algorithm is provided, and the solvent of the defect tracing is explained. Further, based on the validation theorem on the cross iteration, a validation method for simulation models with the cross iteration is proposed, which is illustrated by a flowchart step by step. Finally, a validation example of a sixdegree of freedom (DOF) flight vehicle model is provided, and the validation process is performed by using the validation method. The result analysis shows that the method is effective to obtain the credibility of the model and accomplish the defect tracing of the validation.展开更多
Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusse...Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusses the iteratively B-convergence of the Newton iterative process, finally, the paper provides some numberical results which show that the parallel scheme is highly efficient as N is not too large.展开更多
为设计高效稳定的演化算法,将方程求根的不动点迭代思想引入到优化领域,通过将演化算法的寻优过程看作为在迭代框架下方程不动点的逐步显示化过程,设计出一种基于数学模型的演化新算法,即不动点演化算法(fixed point evolution algorith...为设计高效稳定的演化算法,将方程求根的不动点迭代思想引入到优化领域,通过将演化算法的寻优过程看作为在迭代框架下方程不动点的逐步显示化过程,设计出一种基于数学模型的演化新算法,即不动点演化算法(fixed point evolution algorithm,FPEA).该算法的繁殖算子是由Aitken加速的不动点迭代模型导出的二次多项式,其整体框架继承传统演化算法(如差分演化算法)基于种群的迭代模式.试验结果表明:在基准函数集CEC2014、CEC2019上,本文算法的最优值平均排名在所有比较算法中排名第1;在4个工程约束设计问题上,FPEA与CSA、GPE等多个算法相比,能以较少的计算开销获得最高的求解精度.展开更多
研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导...研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。展开更多
为提升哈里斯鹰优化算法收敛精度,解决易陷入局部最优等问题,提出了一种基于迭代混沌精英反向学习和黄金正弦策略的哈里斯鹰优化算法(gold sine HHO,GSHHO)。利用无限迭代混沌映射初始化种群,运用精英反向学习策略筛选优质种群,提高种...为提升哈里斯鹰优化算法收敛精度,解决易陷入局部最优等问题,提出了一种基于迭代混沌精英反向学习和黄金正弦策略的哈里斯鹰优化算法(gold sine HHO,GSHHO)。利用无限迭代混沌映射初始化种群,运用精英反向学习策略筛选优质种群,提高种群质量,增强算法的全局搜索能力;使用一种收敛因子调整策略重新计算猎物能量,平衡算法的全局探索和局部开发能力;在哈里斯鹰的开发阶段引入黄金正弦策略,替换原有的位置更新方法,提升算法的局部开发能力;在9个测试函数和不同规模的栅格地图上评估GSHHO的有效性。实验结果表明:GSHHO在不同测试函数中具有较好的寻优精度和稳定性能,在2次机器人路径规划中路径长度较原始HHO算法分别减少4.4%、3.17%,稳定性分别提升52.98%、63.12%。展开更多
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
基金supported by National Natural Science Foundation of China(62371225,62371227)。
文摘Linear minimum mean square error(MMSE)detection has been shown to achieve near-optimal performance for massive multiple-input multiple-output(MIMO)systems but inevitably involves complicated matrix inversion,which entails high complexity.To avoid the exact matrix inversion,a considerable number of implicit and explicit approximate matrix inversion based detection methods is proposed.By combining the advantages of both the explicit and the implicit matrix inversion,this paper introduces a new low-complexity signal detection algorithm.Firstly,the relationship between implicit and explicit techniques is analyzed.Then,an enhanced Newton iteration method is introduced to realize an approximate MMSE detection for massive MIMO uplink systems.The proposed improved Newton iteration significantly reduces the complexity of conventional Newton iteration.However,its complexity is still high for higher iterations.Thus,it is applied only for first two iterations.For subsequent iterations,we propose a novel trace iterative method(TIM)based low-complexity algorithm,which has significantly lower complexity than higher Newton iterations.Convergence guarantees of the proposed detector are also provided.Numerical simulations verify that the proposed detector exhibits significant performance enhancement over recently reported iterative detectors and achieves close-to-MMSE performance while retaining the low-complexity advantage for systems with hundreds of antennas.
基金supported by the National Natural Science Foundation of China(61374164)
文摘Cross iteration often exists in the computational process of the simulation models, especially for control models. There is a credibility defect tracing problem in the validation of models with cross iteration. In order to resolve this problem, after the problem formulation, a validation theorem on the cross iteration is proposed, and the proof of the theorem is given under the cross iteration circumstance. Meanwhile, applying the proposed theorem, the credibility calculation algorithm is provided, and the solvent of the defect tracing is explained. Further, based on the validation theorem on the cross iteration, a validation method for simulation models with the cross iteration is proposed, which is illustrated by a flowchart step by step. Finally, a validation example of a sixdegree of freedom (DOF) flight vehicle model is provided, and the validation process is performed by using the validation method. The result analysis shows that the method is effective to obtain the credibility of the model and accomplish the defect tracing of the validation.
文摘Based on the efficient hybrid methods for solving initial value problems of stiff ODEs, this paper derives a parallel scheme that can be used to solve the problems on parallel computers with N processors, and discusses the iteratively B-convergence of the Newton iterative process, finally, the paper provides some numberical results which show that the parallel scheme is highly efficient as N is not too large.
文摘为设计高效稳定的演化算法,将方程求根的不动点迭代思想引入到优化领域,通过将演化算法的寻优过程看作为在迭代框架下方程不动点的逐步显示化过程,设计出一种基于数学模型的演化新算法,即不动点演化算法(fixed point evolution algorithm,FPEA).该算法的繁殖算子是由Aitken加速的不动点迭代模型导出的二次多项式,其整体框架继承传统演化算法(如差分演化算法)基于种群的迭代模式.试验结果表明:在基准函数集CEC2014、CEC2019上,本文算法的最优值平均排名在所有比较算法中排名第1;在4个工程约束设计问题上,FPEA与CSA、GPE等多个算法相比,能以较少的计算开销获得最高的求解精度.
文摘研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。
文摘为提升哈里斯鹰优化算法收敛精度,解决易陷入局部最优等问题,提出了一种基于迭代混沌精英反向学习和黄金正弦策略的哈里斯鹰优化算法(gold sine HHO,GSHHO)。利用无限迭代混沌映射初始化种群,运用精英反向学习策略筛选优质种群,提高种群质量,增强算法的全局搜索能力;使用一种收敛因子调整策略重新计算猎物能量,平衡算法的全局探索和局部开发能力;在哈里斯鹰的开发阶段引入黄金正弦策略,替换原有的位置更新方法,提升算法的局部开发能力;在9个测试函数和不同规模的栅格地图上评估GSHHO的有效性。实验结果表明:GSHHO在不同测试函数中具有较好的寻优精度和稳定性能,在2次机器人路径规划中路径长度较原始HHO算法分别减少4.4%、3.17%,稳定性分别提升52.98%、63.12%。
