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A PARALLEL COMPUTATION SCHEME FOR IMPLICIT RUNGE-KUTTA METHODS AND THE ITERATIVELY B-CONVERGENCE OF ITS NEWTON ITERATIVE PROCESS
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作者 赵双锁 王昌银 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1994年第1期54-66,共13页
In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and di... In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large. 展开更多
关键词 IMPLICIT Range-Kutta methods newton iterative process parallel COMPUTATION iteratively B-CONVERGENCE
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A Newton type iterative method for heat-conduction inverse problems
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作者 贺国强 孟泽红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第4期531-539,共9页
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. ... An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones. 展开更多
关键词 inverse problems nonlinear ill-posed operator equations newton type method implicit iterative method iteration stopping rule
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A SIGNIFICANT IMPROVEMENT ON NEWTON’S ITERATIVE METHOD
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作者 吴新元 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第8期103-106,共4页
For solving nonlinear and transcendental equation f(x)=0 , a singnificant improvement on Newton's method is proposed in this paper. New “Newton Like” methods are founded on the basis of Liapunov's methods... For solving nonlinear and transcendental equation f(x)=0 , a singnificant improvement on Newton's method is proposed in this paper. New “Newton Like” methods are founded on the basis of Liapunov's methods of dynamic system. These new methods preserve quadratic convergence and computational efficiency of Newton's method, and remove the monotoneity condition imposed on f(x):f′(x)≠0 . 展开更多
关键词 nonlinear equation transcendental equation dynamic system iterative method newton's method numerical analysis
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关于Newton-like-iterative方法新的收敛性定理(英文)
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作者 武敏 《浙江科技学院学报》 CAS 2010年第4期241-246,共6页
用迭代法求解Newton-like法中的方程,T.J . Ypma提出Newton-like-iterative方法。在其早期的文章中,不精确牛顿法理论用来研究Newton-like-iterative方法的收敛性。与以往方法不同,今提出用不精确Newton-like法做相关的收敛性分析,所得... 用迭代法求解Newton-like法中的方程,T.J . Ypma提出Newton-like-iterative方法。在其早期的文章中,不精确牛顿法理论用来研究Newton-like-iterative方法的收敛性。与以往方法不同,今提出用不精确Newton-like法做相关的收敛性分析,所得定理更加简单,同时具有仿射不变性。 展开更多
关键词 非线性方程 newton-like方法 newton-like-iterative方法 不精确牛顿法 不精确newton-like方法 仿射不变性
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A Family of Fifth-order Iterative Methods for Solving Nonlinear Equations 被引量:4
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作者 Liu Tian-Bao Cai Hua Li Yong 《Communications in Mathematical Research》 CSCD 2013年第3期255-260,共6页
In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order... In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects. 展开更多
关键词 newton's method iterative method nonlinear equation order of convergence
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ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Ioannis K.ARGYROS Santhosh GEORGE 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1318-1324,共7页
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is... In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping. 展开更多
关键词 nonlinear ill-posed equations iterative regularization m-accretive operator newton type method
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ANCIENT CHINESE ALGORITHM: THE YING BUZU SHU (METHOD OF SURPLUS AND DEFICIENCY)VS NEWTON ITERATION METHOD
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作者 何吉欢 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第12期1407-1412,共6页
Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of dou... Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated. 展开更多
关键词 ancient chinese mathematics Jiuzhang Suanshu (nine chapters) newton iteration method Duffing equation
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Modified Efficient Families of Two and Three-Step Predictor-Corrector Iterative Methods for Solving Nonlinear Equations
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作者 Sanjeev Kumar Vinay Kanwar Sukhjit Singh 《Applied Mathematics》 2010年第3期153-158,共6页
In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods ... In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency. 展开更多
关键词 Nonlinear Equations iterative methodS Multipoint iterative methodS newton’s method Traub-Ostrowski’s method PREDICTOR-CORRECTOR methodS Order of Convergence
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New Fourth Order Iterative Methods Second Derivative Free
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作者 Osama Y. Ababneh 《Journal of Applied Mathematics and Physics》 2016年第3期519-523,共5页
In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574... In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives;therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods. 展开更多
关键词 newton’s method Fourth-Order Convergence Third-Order Convergence Non-Linear Equations ROOT-FINDING iterative method
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Three Modified Efficient Iterative Methods for Non-linear Equations
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作者 Liang Fang Lift Ni Rui Chen 《数学计算(中英文版)》 2013年第1期6-12,共7页
关键词 非线性方程 迭代方法 改良 指数算法 牛顿法 二阶导数 数值结果 收敛
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A Fourth-order Covergence Newton-type Method 被引量:3
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作者 WANG Xia ZHAO Ling-ling 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第4期589-593,共5页
A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton's method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots ... A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton's method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application. 展开更多
关键词 newton iteration method root-finding method fourth-order convergence numerical test
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On Newton-Like Methods for Solving Nonlinear Equations 被引量:1
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作者 KOU Jisheng LIU Dingyou LI Yitian HE Julin 《Geo-Spatial Information Science》 2006年第1期76-78,共3页
In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treat... In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed. 展开更多
关键词 newton method newton-like method nonlinear equations iteration method
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Comparison of Iterative Feedback Tuning Search Techniques 被引量:1
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作者 Graham E. A. Gamage P. 《武汉理工大学学报》 CAS CSCD 北大核心 2006年第S1期62-67,共6页
Iterative feedback tuning is an attractive method for industry as it is a model free approach using experiments conducted on the plant to tune controller parameters. Classically Gauss-Newton iterative methods are used... Iterative feedback tuning is an attractive method for industry as it is a model free approach using experiments conducted on the plant to tune controller parameters. Classically Gauss-Newton iterative methods are used in IFT to update the controller parameters in the negative gradient direction of a specified design criterion function. Levenburg-Marquardt and Trust-Region strategies offer attractive advantages to Gauss-Newton in many applications,these alternative methods are given and results from simulation presented. A discussion on the differences between line search methods and Trust-Region methods is given showing the Trust-Region search direction is more flexible. Step size selection is often the limiting factor and it is found that with unknown step size values and initial controller parameters the Trust-Region is the best selection,where as if overshoot is a concern Levenburg-Marquardt is a good choice.Gauss-Newton method provides quick convergence and a fast response time however it shows more dependence on the step size. 展开更多
关键词 COMPARISON iterative FEEDBACK tuning Gauss-newton method
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The Initial Guess Estimation Newton Method for Power Flow in Distribution Systems
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作者 Qiuye Sun Ling Liu +1 位作者 Dazhong Ma Huaguang Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2017年第2期231-242,共12页
With the increasing integration of distributed generations U+0028 DGs U+0029, there is a demand for DGs to play a more important role on the voltage regulation. Meanwhile, the high penetration of DGs could raise a tec... With the increasing integration of distributed generations U+0028 DGs U+0029, there is a demand for DGs to play a more important role on the voltage regulation. Meanwhile, the high penetration of DGs could raise a technical problem that the distribution system may operate with bi-directional power flow, leading to the inadequacy of the traditional power flow. Considering this new scenario in distribution system power flow, the convergence theorem is proposed, which contributes to develop a novel selection method of the initial guess closed to the convergent solution. Moreover, to ensure the fast rate of power flow convergence, the theorem of the maximum iterations estimation is also proposed. Based on the two proposed theorems, an Initial Guess Estimation Newton method is proposed, considering different operational status of DGs and initial guess sensitivity simultaneously. Based on the standard node systems, Tongliao grid, and 69 system of USA, three simulation examples are provided to illustrate the effectiveness of the proposed method. © 2017 Chinese Association of Automation. 展开更多
关键词 Distributed power generation iterative methods newton Raphson method Voltage regulators
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The Continuous Analogy of Newton’s Method for Solving a System of Linear Algebraic Equations
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作者 Tugal Zhanlav Ochbadrakh Chuluunbaatar Gantumur Ankhbayar 《Applied Mathematics》 2013年第1期210-216,共7页
We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the numb... We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the number of inner iterations in advance. The latter is to use the inexact Newton method for solution of the linear system of equations that arises at each stage of outer iterations. We give some new choices of iteration parameter and of forcing term, that ensure the convergence of iterations. The performance and efficiency of the proposed iteration is illustrated by numerical examples that represent a wide range of typical systems. 展开更多
关键词 CONTINUOUS ANALOGY of newton’s method SOLVING the System of Linear ALGEBRAIC Equations Convergence CHOICE of iterATION Parameter
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A New Modification of Newton Method with Cubic Convergence
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作者 Aurelien Goudjo Louis Kouye 《Advances in Pure Mathematics》 2021年第1期1-11,共11页
Newton’s method is used to find the roots of a system of equations <span style="white-space:nowrap;"><em>f</em> (x) = 0</span>. It is one of the most important procedures in numerica... Newton’s method is used to find the roots of a system of equations <span style="white-space:nowrap;"><em>f</em> (x) = 0</span>. It is one of the most important procedures in numerical analysis, and its applicability extends to differential equations and integral equations. Analysis of the method shows a quadratic convergence under certain assumptions. For several years, researchers have improved the method by proposing modified Newton methods with salutary efforts. A modification of the Newton’s method was proposed by McDougall and Wotherspoon <a href="#ref1">[1]</a> with an order of convergence of <span style="white-space:nowrap;">1+ <span style="white-space:nowrap;">&#8730;2</span></span>. On a new type of methods with cubic convergence was proposed by H. H. H. Homeier <a href="#ref2">[2]</a>. In this article, we present a new modification of Newton method based on secant method. Analysis of convergence shows that the new method is cubically convergent. Our method requires an evaluation of the function and one of its derivatives. 展开更多
关键词 newton’s methods Secant method Cubic Convergence iterative method
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Newton-type methods and their modifications for inverse heat conduction problems
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作者 康传刚 孟泽红 贺国强 《Journal of Shanghai University(English Edition)》 CAS 2010年第3期196-200,共5页
This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several mo... This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs. 展开更多
关键词 nonlinear inverse problem inverse heat conduction problem newton-Tikhonov method newton-implicit iterative method modification
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非精确Newton方法中线性迭代收敛判据研究
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作者 冯选燕 燕振国 +2 位作者 朱华君 马燕凯 冯新龙 《空气动力学学报》 CSCD 北大核心 2023年第12期28-36,共9页
在计算流体力学中,采用隐式时间推进方法时通常需要采用Newton类迭代方法求解大型非线性离散系统。每步非线性迭代需求解由非线性系统Jacobian矩阵组成的大型线性方程组,其中线性方程组求解误差会对非线性系统的收敛性产生显著影响,然... 在计算流体力学中,采用隐式时间推进方法时通常需要采用Newton类迭代方法求解大型非线性离散系统。每步非线性迭代需求解由非线性系统Jacobian矩阵组成的大型线性方程组,其中线性方程组求解误差会对非线性系统的收敛性产生显著影响,然而对存在Jacobian矩阵误差情况下的线性迭代收敛判据缺乏深入的研究。本文针对上述问题,首先给出了存在Jacobian矩阵误差和线性迭代误差情况下Newton迭代式的形式,并通过数值测试验证了Jacobian矩阵误差对迭代产生较大影响的可能性;其次对常见的两种不同类型的线性迭代收敛判据进行了数值测试,重点研究了存在Jacobian矩阵误差情况下容易产生的过度求解问题;最后,结合上述两类判据的特点发展了一种新的线性迭代收敛判据,结果表明:新提出的迭代收敛判据能够有效缓解过度求解问题,从而提高计算效率。 展开更多
关键词 newton方法 隐式时间推进 Jacobian矩阵误差 线性迭代 收敛判据 矩阵刚性 计算流体力学
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基于MATLAB的民航发动机涡轮叶片寿命建模
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作者 袁忠大 程秀全 王大伟 《机床与液压》 北大核心 2024年第4期156-161,共6页
针对民航飞机维修工作中发动机涡轮叶片普遍存在故障率较高的问题,收集某型民用航空发动机涡轮叶片的可靠性数据,并运用三参数Weibull分布建立该型发动机涡轮叶片的可靠性寿命模型。在模型求解的数值计算过程中,为保证模型的计算精度,... 针对民航飞机维修工作中发动机涡轮叶片普遍存在故障率较高的问题,收集某型民用航空发动机涡轮叶片的可靠性数据,并运用三参数Weibull分布建立该型发动机涡轮叶片的可靠性寿命模型。在模型求解的数值计算过程中,为保证模型的计算精度,采用经典的牛顿迭代法及三参数相关系数优化法对涡轮叶片的寿命数据进行拟合分析及计算;同时为减少计算工作量及提高数值计算过程中人工智能的参与度,基于MATLAB软件对上述数值计算方法编写计算程序,最后对计算结果进行K-S假设检验。结果表明:对涡轮叶片寿命数据进行可靠性分析时,运用Weibull分布建立的数学模型符合客观规律;同时牛顿迭代法、三参数相关系数优化法及MATLAB计算程序的有效利用,保证了计算结果的精度。 展开更多
关键词 涡轮叶片 寿命建模 牛顿迭代法 三参数相关系数优化法
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针对十参数标定模型的导航避障相机影像精确校正
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作者 王强 刘阳 +3 位作者 刘思齐 胡迪 崔希民 范生宏 《测绘通报》 CSCD 北大核心 2024年第10期98-102,119,共6页
十参数标定模型是近景摄影测量中一种经典的内参标定模型。在影像畸变校正中,如果利用此模型采用直接重采样方式会产生空洞条纹,而常规的间接重采样方式虽无空洞产生,但在畸变较大的非中心区域同样无法得到较好的校正效果。针对此问题,... 十参数标定模型是近景摄影测量中一种经典的内参标定模型。在影像畸变校正中,如果利用此模型采用直接重采样方式会产生空洞条纹,而常规的间接重采样方式虽无空洞产生,但在畸变较大的非中心区域同样无法得到较好的校正效果。针对此问题,本文提出了一种针对十参数标定模型的影像牛顿迭代精确校正算法。首先利用十参数标定模型将像点理想值和实际值进行重组,构建以像点实际值为待求量的非线性方程组;然后采用牛顿迭代法对影像中畸变部分进行局部线性逼近求解;最后采用间接重采样方法实现精确校正的目的。以移动机器人导航和避障相机作为研究对象,试验结果表明,牛顿迭代法校正可以得到高精度的优质去畸变影像,对避障相机的处理效果尤为显著。本文算法适用于移动机器人导航避障相机影像的畸变精确去除,为后续立体匹配环节生成优质的双目核线影像提供了可靠数据源。 展开更多
关键词 畸变校正 十参数标定模型 牛顿迭代法 导航避障相机
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