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Broyden非凸族的收敛性 被引量:13
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作者 柯小伍 《北京师范大学学报(自然科学版)》 CAS CSCD 1995年第1期6-10,共5页
利用Byrd等人给出的ψ函数,分析了Broyden非凸族.对于一致凸函数,证明了Broyden非凸族的全局和超线性收敛性.
关键词 broyden 非凸族 收敛性 超线性 收敛 凸函数
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基于无标定显微视觉伺服的零件微装配 被引量:5
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作者 曾祥进 黄心汉 王敏 《信息与控制》 CSCD 北大核心 2009年第2期182-186,193,共6页
为完成微小零件的装配操作,获得高效的微装配性能和避免复杂的摄像机标定工作,提出了基于BROYDEN方法的图像雅可比矩阵在线辨识模型.为了实现在线辨识快速收敛的目的,应用切比雪夫多项式构成了待辨识的图像雅可比矩阵的成本函数来逼近... 为完成微小零件的装配操作,获得高效的微装配性能和避免复杂的摄像机标定工作,提出了基于BROYDEN方法的图像雅可比矩阵在线辨识模型.为了实现在线辨识快速收敛的目的,应用切比雪夫多项式构成了待辨识的图像雅可比矩阵的成本函数来逼近最优值.采用辨识的图像雅可比矩阵,设计了PD控制器,该控制器满足了系统的快速性和平滑性控制要求.在显微视觉环境下,完成了不同倍率物镜下微操作机械手自动定位与夹取三维微小零件的视觉伺服任务.实验结果表明,所提方法具有较好的鲁棒性和满意的执行效果,达到了系统应用要求. 展开更多
关键词 微装配 broyden 图像雅可比矩阵辨识 视觉控制器 显微视觉伺服
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SVM-based Identification and Un-calibrated Visual Servoing for Micro-manipulation 被引量:3
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作者 Xin-Han Huang Xiang-Jin Zeng Min Wang Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PRC 《International Journal of Automation and computing》 EI 2010年第1期47-54,共8页
This paper presents an improved support vector machine (SVM) algorithm, which employs invariant moments-based edge extraction to obtain feature attribute. A heuristic attribute reduction algorithm based on rough set... This paper presents an improved support vector machine (SVM) algorithm, which employs invariant moments-based edge extraction to obtain feature attribute. A heuristic attribute reduction algorithm based on rough set's discernible matrix is proposed to identify and classify micro-targets. To avoid the complicated calibration for intrinsic parameters of camera, an improved Broyden's method is proposed to estimate the image Jacobian matrix which employs Chebyshev polynomial to construct a cost function to approximate the optimization value. Finally, a visual controller is designed for a robotic micromanipulation system. The experiment results of micro-parts assembly show that the proposed methods and algorithms are effective and feasible. 展开更多
关键词 MICRO-ASSEMBLY support vector machine part identification broyden method visual servoing
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Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet 被引量:2
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作者 Bikash SAHOO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第2期159-173,共15页
The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip fa... The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields. 展开更多
关键词 second grade fluid stretching sheet partial slip heat transfer finitedifference method broyden's method
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AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method
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作者 Isaac Azure Japheth Kodua Wiredu +1 位作者 Anas Musah Eric Akolgo 《American Journal of Computational Mathematics》 2023年第4期644-677,共34页
This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core obj... This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python’s failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifications in real-world applications. The choice between Python and MATLAB can yield distinct advantages depending on the specific problem and computational environment, providing guidance for 展开更多
关键词 System of Nonlinear Equations broyden Method Robustness Index Artificial Intelligence (AI) MATLAB SCILAB PYTHON
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Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch 被引量:1
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作者 Da-chuan XuInstitute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2003年第1期19-24,共6页
Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under ... Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved. 展开更多
关键词 Keywords Quasi-Newton method broyden class non-monotone linesearch global convergence unconstrained optimization
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基于Broyden法的非线性电阻电路分析
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作者 付裕 《集成电路应用》 2023年第1期114-115,共2页
阐述将数值法中的Broyden法应用到非线性电阻电路的分析与求解中,并且将Broyden法与牛顿法进行对比。通过实例发现Broyden法完全可以应用于求解非线性电路中,而且Broyden法要比牛顿法具有更高的精度、更少的雅克比矩阵计算次数。
关键词 电路分析 非线性电阻电路 broyden
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Alternate Broyden's Method for Solving Linear Least Squares Problem with Multiple Right-Hand Sides
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作者 顾桂定 《Advances in Manufacturing》 SCIE CAS 1997年第3期196-201,共6页
In this paper, we extend the alternate Broyden's method to the multiple version fbi solving lincar leastsquarc systems with multiple right-hand sides. We show that the method possesses property of a finite tcrmina... In this paper, we extend the alternate Broyden's method to the multiple version fbi solving lincar leastsquarc systems with multiple right-hand sides. We show that the method possesses property of a finite tcrmination.Some numerical cxperiments are gi von to inustrate the effectiveness of the method. 展开更多
关键词 mnltiple version of the broyden's broyden's alternate broyden's method linear least squares problem finte termination
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Models and Algorithms for Diffuse Optical Tomographic System
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作者 Samir Kumar Biswas Rajan Kanhirodan Ram Mohan Vasu 《International Journal of Communications, Network and System Sciences》 2013年第12期489-496,共8页
Diffuse optical tomography (DOT) using near-infrared (NIR) light is a promising tool for noninvasive imaging of deep tissue. The approach is capable of reconstructing the quantitative optical parameters (absorption co... Diffuse optical tomography (DOT) using near-infrared (NIR) light is a promising tool for noninvasive imaging of deep tissue. The approach is capable of reconstructing the quantitative optical parameters (absorption coefficient and scattering coefficient) of a soft tissue. The motivation for reconstructing the optical property variation is that it and, in particular, the absorption coefficient variation, can be used to diagnose different metabolic and disease states of tissue. In DOT, like any other medical imaging modality, the aim is to produce a reconstruction with good spatial resolution and in contrast with noisy measurements. The parameter recovery known as inverse problem in highly scattering biological tissues is a nonlinear and ill-posed problem and is generally solved through iterative methods. The algorithm uses a forward model to arrive at a prediction flux density at the tissue boundary. The forward model uses light transport models such as stochastic Monte Carlo simulation or deterministic methods such as radioactive transfer equation (RTE) or a simplified version of RTE namely the diffusion equation (DE). The finite element method (FEM) is used for discretizing the diffusion equation. The frequently used algorithm for solving the inverse problem is Newton-based Model based Iterative Image Reconstruction (N-MoBIIR). Many Variants of Gauss-Newton approaches are proposed for DOT reconstruction. The focuses of such developments are 1) to reduce the computational complexity;2) to improve spatial recovery;and 3) to improve contrast recovery. These algorithms are 1) Hessian based MoBIIR;2) Broyden-based MoBIIR;3) adjoint Broyden-based MoBIIR;and 4) pseudo-dynamic approaches. 展开更多
关键词 DIFFUSE OPTICAL Tomography GAUSS NEWTON Methods broyden and ADJOINT broyden Approaches Pseu-do-Dynamic Method
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M-TIMES SECANT-LIKE MULTI-PROJCTION METHOD FOR SPARSE MINIMIZATION PROBLEM
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作者 林正华 宋岱才 赵立芹 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2001年第1期26-36,共11页
In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we f... In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we from some numerical results, discuss how to choose the number m to determine the approximating matrix properly in practical use. 展开更多
关键词 Sparse optimization problem superlinear convergence sparse symmetric broyden method m time secant-like multi projection method.
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Comparing two iteration algorithms of Broyden electron density mixing through an atomic electronic structure computation
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作者 张满红 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第5期126-131,共6页
By performing the electronic structure computation of a Si atom, we compare two iteration algorithms of Broyden electron density mixing in the literature. One was proposed by Johnson and implemented in the well-known ... By performing the electronic structure computation of a Si atom, we compare two iteration algorithms of Broyden electron density mixing in the literature. One was proposed by Johnson and implemented in the well-known VASP code.The other was given by Eyert. We solve the Kohn-Sham equation by using a conventional outward/inward integration of the differential equation and then connect two parts of solutions at the classical turning points, which is different from the method of the matrix eigenvalue solution as used in the VASP code. Compared to Johnson's algorithm, the one proposed by Eyert needs fewer total iteration numbers. 展开更多
关键词 self-consistent field electron density mixing broyden algorithm density functional
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Sparse two-sided rank-one updates for nonlinear equations
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作者 CHENG MingHou & DAI YuHong State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 《Science China Mathematics》 SCIE 2010年第11期2907-2915,共9页
The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale spa... The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale sparse problems. To overcome this difficulty, we propose sparse extensions of the TR1 update and give some convergence analysis. The numerical experiments show that some of our extensions are superior to the TR1 update method. Some convergence analysis is also presented. 展开更多
关键词 TR1 UPDATE broyden rank-one UPDATE SPARSITY
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A Variable Metric Algorithm with Broyden Rank One Modifications for Nonlinear Equality Constraints Optimization
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作者 Chunyan Hu Zhibin Zhu 《Open Journal of Optimization》 2013年第1期33-37,共5页
In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton met... In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton method to unconstrained optimization. The theoretical analysis shows that local convergence can be induced under some suitable conditions. In the end, it is established an equivalent condition of superlinear convergence. 展开更多
关键词 EQUALITY Constrained OPTIMIZATION Variable Metric Algorithm broyden RANK ONE Modification SUPERLINEAR Convergence
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分布式CFAR检测系统的最优门限求取新方法
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作者 韩志钢 魏玺章 黎湘 《电光与控制》 北大核心 2012年第8期20-22,27,共4页
针对并行分布式检测网络结构局部采用CFAR检测器的情形,提出了一种在融合规则给定时,局部CFAR检测器最优门限的求取方法。给出了在任意融合规则下融合中心的检测概率和虚警概率关于局部门限的一阶导数的数值计算公式,并利用Broyden方法... 针对并行分布式检测网络结构局部采用CFAR检测器的情形,提出了一种在融合规则给定时,局部CFAR检测器最优门限的求取方法。给出了在任意融合规则下融合中心的检测概率和虚警概率关于局部门限的一阶导数的数值计算公式,并利用Broyden方法求取最优的局部门限。该方法避免了传统方法需要计算二阶导数的复杂性,并且更容易推广到局部采用多类CFAR检测器的情形。实验分析表明了算法的有效性。 展开更多
关键词 分布式CFAR检测 并行网络 最优门限 broyden
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THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION
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作者 PU Dingguo(Institute of Applied Mathematics, Shanghai Tiedao University, Shanghai 200333, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1997年第4期289-298,共10页
In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent... In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent point sequence, then the limitpoint of the sequence is a critical point of the objective function. 展开更多
关键词 broyden algorithms CONVERGENCE CONVEXITY EXACT line search.
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Global and Superlinear Convergence for Generalized Broyden's Class Methods
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作者 ZHAO Yunbin(Chongqing Industry and Management Institute. Chongqing, 630050. China) 《Systems Science and Systems Engineering》 CSCD 1994年第2期175-184,共10页
Generalized Broyden’s class methods Presented by this paper is a new class Newton-like method. The global and superlinear convergence Of the method with inexact and exact line search are proved, when applied to a uni... Generalized Broyden’s class methods Presented by this paper is a new class Newton-like method. The global and superlinear convergence Of the method with inexact and exact line search are proved, when applied to a uniformly convex objection function. 展开更多
关键词 unconstrained optimization generalized broyden’s class method global and superlinearconvergence. Wolfe rule.
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A Gauss-Newton-Based Broyden’s Class Algorithm for Parameters of Regression Analysis
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作者 Xiangrong Li Xupei Zhao 《Applied Mathematics》 2011年第1期39-46,共8页
In this paper, a Gauss-Newton-based Broyden’s class method for parameters of regression problems is presented. The global convergence of this given method will be established under suitable conditions. Numerical resu... In this paper, a Gauss-Newton-based Broyden’s class method for parameters of regression problems is presented. The global convergence of this given method will be established under suitable conditions. Numerical results show that the proposed method is interesting. 展开更多
关键词 GLOBAL CONVERGENCE broyden’s CLASS Regression Analysis NONLINEAR EQUATIONS Gauss-Newton
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基于图像特征偏差的姿态调整策略研究
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作者 刘延杰 景亚宁 隋聪颖 《机械与电子》 2014年第8期66-70,共5页
为了实现对泡沫柱空间姿态的调整,研究了基于双路视觉的泡沫柱空间位姿调整策略,建立了系统的运动学模型,在此基础上,提出了基于图像特征偏差的位姿调整策略。在仿真分析中,推导了基于Broyden方法的图像雅可比矩阵在线估计方程,建立了... 为了实现对泡沫柱空间姿态的调整,研究了基于双路视觉的泡沫柱空间位姿调整策略,建立了系统的运动学模型,在此基础上,提出了基于图像特征偏差的位姿调整策略。在仿真分析中,推导了基于Broyden方法的图像雅可比矩阵在线估计方程,建立了系统的运动学模型与视觉成像模型,设计采用了比例控制器。仿真结果表明,采用的图像雅可比矩阵估计方法可以很好地跟踪目标图像特征,图像特征偏差可以快速收敛到设定要求。 展开更多
关键词 姿态调整 图像特征 图像雅可比矩阵 broyden 方法
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A CLASS OF DECOMPOSITION METHODS FOR LARGE-SCALE SYSTEMS OF NONLINEAR EQUATIONS
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作者 王德人 张建军 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1997年第1期90-106,共17页
This paper presents a new decomposition method for solving large-scale systems of nonlinear equations. The new method is of superlinear convergence speed and has rather less computa tional complexity than the Newton-t... This paper presents a new decomposition method for solving large-scale systems of nonlinear equations. The new method is of superlinear convergence speed and has rather less computa tional complexity than the Newton-type decomposition method as well as other known numerical methods, Primal numerical experiments show the superiority of the new method to the others. 展开更多
关键词 Systems of nonlinear EQUATIONS SUPERLINEAR CONVERGENCE broyden’s UPDATE COLUMN UPDATE DECOMPOSITION method.
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Efficient Numerical Scheme for the Solution of HIV Infection CD4^(+)T-Cells Using Haar Wavelet Technique
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作者 Rohul Amin Suayip Yuzbasi Shah Nazir 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第5期639-653,共15页
In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells model.In this technique,the derivative in the nonlinear model is approximated by utilizing Haar funct... In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells model.In this technique,the derivative in the nonlinear model is approximated by utilizing Haar functions.The value of the unknown function is obtained by the process of integration.Error estimation is also discussed,which aims to reduce the error of numerical solutions.The numerical results show that the method is simply applicable.The results are compared with Runge-Kutta technique,Bessel collocation technique,LADM-Pade and Galerkin technique available in the literature.The results show that the Haar technique is easy,precise and effective. 展开更多
关键词 System of nonlinear differential equations HIV infection of CD4^(+)T-cells broyden method Haar wavelet residual error estimation
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